Search results for: nonlinear partial differential equations

Authors: R. Loukil, M. Chtourou, T. Damak

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In this work, we use the Fault detection and isolation and the Fault tolerant control based on sliding mode observer in order to introduce the well diagnosis of a nonlinear system. The robustness of the proposed observer for the two techniques is tested through a physical example. The results in this paper show the interaction between the Fault tolerant control and the Diagnosis procedure.

Keywords: Fault detection and isolation “FDI”, Fault tolerant control “FTC”, sliding mode observer, nonlinear system, robustness, stability.

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Authors: Swarniv Chandra, Sibarjun Das, Agniv Chandra, Basudev Ghosh, Apratim Jash

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Using the quantum hydrodynamic (QHD) model the nonlinear properties of ion-acoustic waves in are lativistically degenerate quantum plasma is investigated by deriving a nonlinear Spherical Kadomtsev–Petviashvili (SKP) equation using the standard reductive perturbation method equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of ion-acoustic waves in quantum plasma.

Keywords: Kadomtsev-Petviashvili equation, Ion-acoustic Waves, Relativistic Degeneracy, Quantum Plasma, Quantum Hydrodynamic Model.

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

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Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter N_rc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method is found to be good.

Keywords: Convective boundary, radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate.

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Authors: Nikolay Nikolaev, Evgueni Smirnov

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This paper develops an unscented grid-based filter and a smoother for accurate nonlinear modeling and analysis of time series. The filter uses unscented deterministic sampling during both the time and measurement updating phases, to approximate directly the distributions of the latent state variable. A complementary grid smoother is also made to enable computing of the likelihood. This helps us to formulate an expectation maximisation algorithm for maximum likelihood estimation of the state noise and the observation noise. Empirical investigations show that the proposed unscented grid filter/smoother compares favourably to other similar filters on nonlinear estimation tasks.

Keywords:

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Authors: T. Sanches, K. Bousson

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As part of the development of a 4D autopilot system for unmanned aerial vehicles (UAVs), i.e. a time-dependent robust trajectory generation and control algorithm, this work addresses the problem of optimal path control based on the flight sensors data output that may be unreliable due to noise on data acquisition and/or transmission under certain circumstances. Although several filtering methods, such as the Kalman-Bucy filter or the Linear Quadratic Gaussian/Loop Transfer Recover Control (LQG/LTR), are available, the utter complexity of the control system, together with the robustness and reliability required of such a system on a UAV for airworthiness certifiable autonomous flight, required the development of a proper robust filter for a nonlinear system, as a way of further mitigate errors propagation to the control system and improve its ,performance. As such, a nonlinear algorithm based upon the LQG/LTR, is validated through computational simulation testing, is proposed on this paper.

Keywords: Autonomous flight, LQG/LTR, nonlinear state estimator, robust flight control and stability.

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Authors: T. D. Gunneswara Rao, Mudimby Andal

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Research on the utilization of fly ash will no longer refer the fly ash as a waste material of thermal power plants. Use of fly ash in concrete making, makes the concrete economical as well as durable. The fly ash is being added to the concrete in three ways namely, as partial replacement to cement, as partial replacement to fine aggregates and as admixture. Addition of fly ash to the concrete in any one of the form mentioned above, makes the concrete more workable and durable than the conventional concrete. Studies on fly ash as partial replacement to cement gained momentum as such replacement makes the concrete economical. In the present study, an attempt has been made to understand the effects of fly ash on the workability characteristics and strength aspects of fly ash concretes. In India major number of thermal power plants is producing low calcium fly ash. Hence in the present investigation low calcium fly ash has been used. Fly ash in concrete was considered for the partial replacement of cement. The percentage replacement of cement by fly ash varied from 0% to 40% at regular intervals of 10%. More over the fine aggregate to coarse aggregate ratio also has been varied as 1:1, 1:2 and 1:3. The workability tests revealed that up to 30% replacement of cement by fly ash in concrete mixes water demand for reduces, beyond 30% replacement of cement by fly ash demanded more water content for constant workability.

Keywords: Cementing Efficiency, Compressive Strength, Low Calcium Fly Ash, Workability.

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Authors: Khalil Ur Rehman, M. Y. Malik, Usman Ali

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In this paper, the problem proposed by Von Karman is treated in the attendance of additional flow field effects when the liquid is spaced above the rotating rigid disk. To be more specific, a purely viscous fluid flow yield by rotating rigid disk with Navier’s condition is considered in both magnetohydrodynamic and hydrodynamic frames. The rotating flow regime is manifested with heat source/sink and chemically reactive species. Moreover, the features of thermophoresis and Brownian motion are reported by considering nanofluid model. The flow field formulation is obtained mathematically in terms of high order differential equations. The reduced system of equations is solved numerically through self-coded computational algorithm. The pertinent outcomes are discussed systematically and provided through graphical and tabular practices. A simultaneous way of study makes this attempt attractive in this sense that the article contains dual framework and validation of results with existing work confirms the execution of self-coded algorithm for fluid flow regime over a rotating rigid disk.

Keywords: Nanoparticles, Newtonian fluid model, chemical reaction, heat source/sink.

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: Equivalent Martingale Measure, European Put Option, Girsanov Theorem, Martingales, Monte Carlo method, option price valuation, option price valuation formula.

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Authors: T. H. Lee, J. H. Park, S. M. Lee, S. C. Lee

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In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of load current is the significant one of these for good performance of the SOFC system. In order to keep the constant stack terminal voltage by changing load current, the nonlinear model predictive control (MPC) is proposed in this paper. After primary control method is designed to guarantee the fuel utilization as a proper constant, a nonlinear model predictive control based on the Wiener model is developed to control the stack terminal voltage of the SOFC system. Simulation results verify the possibility of the proposed Wiener model and MPC method to control of SOFC system.

Keywords: SOFC, model predictive control, Wiener model.

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Authors: Hideki Yoshikawa, Masahiro Kaminaga, Arimitsu Shikoda, Toshinori Suzuki

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Round addition differential fault analysis using operation skipping for lightweight block ciphers with on-the-fly key scheduling is presented. For 64-bit KLEIN, it is shown that only a pair of correct and faulty ciphertexts can be used to derive the secret master key. For PRESENT, one correct ciphertext and two faulty ciphertexts are required to reconstruct the secret key. Furthermore, secret key extraction is demonstrated for the LBlock Feistel-type lightweight block cipher.

Keywords: Differential Fault Analysis (DFA), round addition, block cipher, on-the-fly key schedule.

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Authors: E. Srinivasan, D. Ebenezer

Abstract:

Midpoint filter is quite effective in recovering the images confounded by the short-tailed (uniform) noise. It, however, performs poorly in the presence of additive long-tailed (impulse) noise and it does not preserve the edge structures of the image signals. Median smoother discards outliers (impulses) effectively, but it fails to provide adequate smoothing for images corrupted with nonimpulse noise. In this paper, two nonlinear techniques for image filtering, namely, New Filter I and New Filter II are proposed based on a nonlinear high-pass filter algorithm. New Filter I is constructed using a midpoint filter, a highpass filter and a combiner. It suppresses uniform noise quite well. New Filter II is configured using an alpha trimmed midpoint filter, a median smoother of window size 3x3, the high pass filter and the combiner. It is robust against impulse noise and attenuates uniform noise satisfactorily. Both the filters are shown to exhibit good response at the image boundaries (edges). The proposed filters are evaluated for their performance on a test image and the results obtained are included.

Keywords: Image filters, Midpoint filter, Nonlinear filters, Nonlinear highpass filter, Order-statistic filters, Rank-order filters.

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Authors: Ahmed Abbas Helmy, M. R. M. Rizk, Mohamed El-Sayed

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A model predictive controller based on recursive learning is proposed. In this SISO adaptive controller, a model is automatically updated using simple recursive equations. The identified models are then stored in the memory to be re-used in the future. The decision for model update is taken based on a new control performance index. The new controller allows the use of simple linear model predictive controllers in the control of nonlinear time varying processes.

Keywords: Adaptive control, model predictive control, dynamic matrix control, online model identification

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Authors: Sameh E. Ahmed, Ramadan A. Mohamed, Abd Elraheem M. Aly, Mahmoud S. Soliman

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In this paper, an enhancement of the heat transfer using non-Newtonian nanofluids by magnetohydrodynamic (MHD) mixed convection along stretching sheets embedded in an isotropic porous medium is investigated. Case of the Maxwell nanofluids is studied using the two phase mathematical model of nanofluids and the Darcy model is applied for the porous medium. Important effects are taken into account, namely, non-linear thermal radiation, convective boundary conditions, electromagnetic force and presence of the heat source/sink. Suitable similarity transformations are used to convert the governing equations to a system of ordinary differential equations then it is solved numerically using a fourth order Runge-Kutta method with shooting technique. The main results of the study revealed that the velocity profiles are decreasing functions of the Darcy number, the Deborah number and the magnetic field parameter. Also, the increase in the non-linear radiation parameters causes an enhancement in the local Nusselt number.

Keywords: MHD, nanofluids, stretching surface, non-linear thermal radiation, convective condition.

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Authors: E. Farshidi

Abstract:

This paper presents the design of a low power second-order continuous-time sigma-delta modulator for low power applications. The loop filter of this modulator has been implemented based on the nonlinear transconductance-capacitor (Gm-C) by employing current-mode technique. The nonlinear transconductance uses floating gate MOS (FG-MOS) transistors that operate in weak inversion region. The proposed modulator features low power consumption (<80uW), low supply voltage (1V) and 62dB dynamic range. Simulation results by HSPICE confirm that it is very suitable for low power biomedical instrumentation designs.

Keywords: Sigma-delta, modulator, Current-mode, Nonlinear Transconductance, FG-MOS.

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Authors: Mao Wei

Abstract:

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.

Keywords: Stochastic age-dependent population equations, poisson random measures, numerical solutions, exponential stability.

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Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam

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Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.

Keywords: Heat conduction, Cellular automata, convergencerate, discrete system.

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Authors: Zachariah Sinkala

Abstract:

A systems approach model for prostate cancer in prostate duct, as a sub-system of the organism is developed. It is accomplished in two steps. First this research work starts with a nonlinear system of coupled Fokker-Plank equations which models continuous process of the system like motion of cells. Then extended to PDEs that include discontinuous processes like cell mutations, proliferation and deaths. The discontinuous processes is modeled by using intensity poisson processes. The model incorporates the features of the prostate duct. The system of PDEs spatial coordinate is along the proximal distal axis. Its parameters depend on features of the prostate duct. The movement of cells is biased towards distal region and mutations of prostate cancer cells is localized in the proximal region. Numerical solutions of the full system of equations are provided, and are exhibit traveling wave fronts phenomena. This motivates the use of the standard transformation to derive a canonically related system of ODEs for traveling wave solutions. The results obtained show persistence of prostate cancer by showing that the non-negative cone for the traveling wave system is time invariant. The traveling waves have a unique global attractor is proved also. Biologically, the global attractor verifies that evolution of prostate cancer stem cells exhibit the avascular tumor growth. These numerical solutions show that altering prostate stem cell movement or mutation of prostate cancer cells lead to avascular tumor. Conclusion with comments on clinical implications of the model is discussed.

Keywords: Fokker-Plank equations, global attractor, stem cell.

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Authors: Saleh S. Hamad Elawgali

Abstract:

Current spectrums of a high power induction machine was calculated for the cases of full symmetry, static and dynamic eccentricity. The calculations involve integration of 93 electrical plus four mechanical ordinary differential equations. Electrical equations account for variable inductances affected by slotting and eccentricities. The calculations were followed by Fourier analysis of the stator currents in steady state operation. The paper presents the stator current spectrums in full symmetry, static and dynamic eccentricity cases, and demonstrates the harmonics present in each case. The effect of dynamic eccentricity is demonstrating via comparing the current spectrums related to dynamic eccentricity cases with the full symmetry one. The paper includes one case study, refers to dynamic eccentricity, to present the spectrum of the measured current and demonstrate the existence of the harmonics related to dynamic eccentricity. The zooms of current spectrums around the main slot harmonic zone are included to simplify the comparison and prove the existence of the dynamic eccentricity harmonics in both calculated and measured current spectrums.

Keywords: Current spectrum, diagnostics, harmonics, Induction machine

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Authors: M. Mohebbi, K. Shakeri

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Since the actuator capacity is limited, in the real application of active control systems under sever earthquakes it is conceivable that the actuators saturate, hence the actuator saturation should be considered as a constraint in design of optimal controllers. In this paper optimal design of active controllers for nonlinear structures by considering actuator saturation, has been studied. The proposed method for designing optimal controllers is based on defining an optimization problem which the objective has been to minimize the maximum displacement of structure when a limited capacity for actuator has been used. To this end a single degree of freedom (SDF) structure with a bilinear hysteretic behavior has been simulated under a white noise ground acceleration of different amplitudes. Active tendon control mechanism, comprised of prestressed tendons and an actuator, and extended nonlinear Newmark method based instantaneous optimal control algorithm have been used. To achieve the best results, the weights corresponding to displacement, velocity, acceleration and control force in the performance index have been optimized by the Distributed Genetic Algorithm (DGA). Results show the effectiveness of the proposed method in considering actuator saturation. Also based on the numerical simulations it can be concluded that the actuator capacity and the average value of required control force are two important factors in designing nonlinear controllers which consider the actuator saturation.

Keywords: Active control, Actuator Saturation, Distributedgeneticalgorithms, Nonlinear.

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Authors: R. Ramaprabha

Abstract:

This paper presents an extraction of maximum energy from Solar Photovoltaic Array (SPVA) under partial shaded conditions by optimum selection of array size using Particle Swarm Optimization (PSO) technique. In this paper a detailed study on the output reduction of different SPVA configurations under partial shaded conditions have been carried out. A generalized MATLAB M-code based software model has been used for any required array size, configuration, shading patterns and number of bypass diodes. Comparative study has been carried out on different configurations by testing several shading scenarios. While the number of shading patterns and the rate of change are very low for stationary SPVA but these may be quite large for SPVA mounted on a mobile platforms. This paper presents the suitability of PSO technique to select optimum configuration for mobile arrays by calculating the global peak (GP) of different configurations and to transfer maximum power to the load.

Keywords: Global peak, Mobile PV arrays, Partial shading, optimization, PSO.

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Authors: Abida Harbi

Abstract:

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic boundary value problem of the form -Δu = f(u), on two overlapping sub domains with non matching grids. We consider a domain which is the union of two overlapping sub domains where each sub domain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz assumption on the nonlinearity, we establish, on each sub domain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the boundary value problem.

Keywords: Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.

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Authors: Akash Rathee, Harish Parthasarathy

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In this paper, a frequency-variation based method has been proposed for transistor parameter estimation in a commonemitter transistor amplifier circuit. We design an algorithm to estimate the transistor parameters, based on noisy measurements of the output voltage when the input voltage is a sine wave of variable frequency and constant amplitude. The common emitter amplifier circuit has been modelled using the transistor Ebers-Moll equations and the perturbation technique has been used for separating the linear and nonlinear parts of the Ebers-Moll equations. This model of the amplifier has been used to determine the amplitude of the output sinusoid as a function of the frequency and the parameter vector. Then, applying the proposed method to the frequency components, the transistor parameters have been estimated. As compared to the conventional time-domain least squares method, the proposed method requires much less data storage and it results in more accurate parameter estimation, as it exploits the information in the time and frequency domain, simultaneously. The proposed method can be utilized for parameter estimation of an analog device in its operating range of frequencies, as it uses data collected from different frequencies output signals for parameter estimation.

Keywords: Perturbation Technique, Parameter estimation, frequency-variation based method.

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Authors: Said Laachir, Aziz Laaribi

Abstract:

The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

Keywords: Helmholtz equation, Nikiforov-Uvarov method, exact solutions, eigenfunctions.

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Authors: Meng Hu, Lili Wang

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In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman-s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays and impulses. An example is given to illustrate the main results.

Keywords: Almost periodic solution, exponential stability, neural networks, impulses.

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Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

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This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: Ruhaya Atan, Saunah Zainon, Roland Yeow Theng Nam, Sharifah Aliman

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This study examines the relevance of disclosure practices in improving the accountability and transparency of religious nonprofit organizations (RNPOs). The assessment of disclosure is based on the annual returns of RNPOs for the financial year 2010. In order to quantify the information disclosed in the annual returns, partial disclosure indexes of basic information (BI) disclosure index, financial information (FI) disclosure index and governance information (GI) disclosure index have been built which takes into account the content of information items in the annual returns. The empirical evidence obtained revealed low disclosure practices among RNPOs in the sample. The multiple regression results showed that the organizational attribute of the board size appeared to be the most significant predictor for both partial index on the extent of BI disclosure index, and FI disclosure index. On the other hand, the extent of financial information disclosure is related to the amount of donation received by RNPOs. On GI disclosure index, the existence of an external audit appeared to be significant variable. This study has contributed to the academic literature in providing empirical evidence of the disclosure practices among RNPOs.

Keywords: disclosure, index, partial, NPOs, religious

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: Differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot.

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Authors: Yaw-Juen Wang, Po-Chun Hsu

Abstract:

This paper presents an equivalent circuit model based on piecewise linear parallel branches (PLPB) to study solar cell modules which are partially shaded. The PLPB model can easily be used in circuit simulation software such as the ElectroMagnetic Transients Program (EMTP). This PLPB model allows the user to simulate several different configurations of solar cells, the influence of partial shadowing on a single or multiple cells, the influence of the number of solar cells protected by a bypass diode and the effect of the cell connection configuration on partial shadowing.

Keywords: Cell Connection Configurations, EMTP, Equivalent Circuit, Partial Shading, Photovoltaic Module

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Authors: Hyun-Woo Cho

Abstract:

The early diagnostic decision making in industrial processes is absolutely necessary to produce high quality final products. It helps to provide early warning for a special event in a process, and finding its assignable cause can be obtained. This work presents a hybrid diagnostic schmes for batch processes. Nonlinear representation of raw process data is combined with classification tree techniques. The nonlinear kernel-based dimension reduction is executed for nonlinear classification decision boundaries for fault classes. In order to enhance diagnosis performance for batch processes, filtering of the data is performed to get rid of the irrelevant information of the process data. For the diagnosis performance of several representation, filtering, and future observation estimation methods, four diagnostic schemes are evaluated. In this work, the performance of the presented diagnosis schemes is demonstrated using batch process data.

Keywords: Diagnostics, batch process, nonlinear representation, data filtering, multivariate statistical approach

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Authors: M. Polanský

Abstract:

This paper introduces a new method called ARPDC (Advanced Robust Parallel Distributed Compensation) for automatic control of nonlinear systems. This method improves a quality of robust control by interpolating of robust and optimal controller. The weight of each controller is determined by an original criteria function for model validity and disturbance appreciation. ARPDC method is based on nonlinear Takagi-Sugeno (T-S) fuzzy systems and Parallel Distributed Compensation (PDC) control scheme. The relaxed stability conditions of ARPDC control of nominal system have been derived. The advantages of presented method are demonstrated on the inverse pendulum benchmark problem. From comparison between three different controllers (robust, optimal and ARPDC) follows, that ARPDC control is almost optimal with the robustness close to the robust controller. The results indicate that ARPDC algorithm can be a good alternative not only for a robust control, but in some cases also to an adaptive control of nonlinear systems.

Keywords: Robust control, optimal control, Takagi–Sugeno (TS) fuzzy models, linear matrix inequality (LMI), observer, Advanced Robust Parallel Distributed Compensation (ARPDC).

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