Search results for: LMI.
52 Robust H8 Fuzzy Control Design for Nonlinear Two-Time Scale System with Markovian Jumps based on LMI Approach
Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang
Abstract:
This paper examines the problem of designing a robust H8 state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H8 performance are derived. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear two-time scale systems. A numerical example is provided to illustrate the design developed in this paper.
Keywords: TS fuzzy, Markovian jumps, LMI, two-time scale systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 148251 Robust H State-Feedback Control for Uncertain Fuzzy Markovian Jump Systems: LMI-Based Design
Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang
Abstract:
This paper investigates the problem of designing a robust state-feedback controller for a class of uncertain Markovian jump nonlinear systems that guarantees the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value. First, we approximate this class of uncertain Markovian jump nonlinear systems by a class of uncertain Takagi-Sugeno fuzzy models with Markovian jumps. Then, based on an LMI approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear systems to have an H performance are derived. An illustrative example is used to illustrate the effectiveness of the proposed design techniques.
Keywords: Robust H, Fuzzy Control, Markovian Jump Systems, LMI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 149850 H∞ Approach to Functional Projective Synchronization for Chaotic Systems with Disturbances
Authors: S. M. Lee, J. H. Park, H. Y. Jung
Abstract:
This paper presents a method for functional projective H∞ synchronization problem of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both drive and response systems but also reduce the effect of external disturbance to an H∞ norm constraint.
Keywords: Chaotic systems, functional projective H∞ synchronization, LMI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 134949 Asymptotic Stability of Input-saturated System with Linear-growth-bound Disturbances via Variable Structure Control: An LMI Approach
Authors: Yun Jong Choi, Nam Woong, PooGyeon Park
Abstract:
Variable Structure Control (VSC) is one of the most useful tools handling the practical system with uncertainties and disturbances. Up to now, unfortunately, not enough studies on the input-saturated system with linear-growth-bound disturbances via VSC have been presented. Therefore, this paper proposes an asymp¬totic stability condition for the system via VSC. The designed VSC controller consists of two control parts. The linear control part plays a role in stabilizing the system, and simultaneously, the nonlinear control part in rejecting the linear-growth-bound disturbances perfectly. All conditions derived in this paper are expressed with Linear Matrices Inequalities (LMIs), which can be easily solved with an LMI toolbox in MATLAB.
Keywords: Input saturation, linear-growth bounded disturbances, linear matrix inequality (LMI), variable structure control
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 167748 Robust H∞ Filter Design for Uncertain Fuzzy Descriptor Systems: LMI-Based Design
Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang
Abstract:
This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.
Keywords: H∞ control, Takagi-Sugeno (TS) fuzzy model, Linear Matrix Inequalities (LMIs), Descriptor systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 142847 Delay-Dependent Stability Analysis for Neural Networks with Distributed Delays
Authors: Qingqing Wang, Shouming Zhong
Abstract:
This paper deals with the problem of delay-dependent stability for neural networks with distributed delays. Some new sufficient condition are derived by constructing a novel Lyapunov-Krasovskii functional approach. The criteria are formulated in terms of a set of linear matrix inequalities, this is convenient for numerically checking the system stability using the powerful MATLAB LMI Toolbox. Moreover, in order to show the stability condition in this paper gives much less conservative results than those in the literature, numerical examples are considered.
Keywords: Neural networks, Globally asymptotic stability , LMI approach, Distributed delays.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 159246 Stability Criteria for Neural Networks with Two Additive Time-varying Delay Components
Authors: Qingqing Wang, Shouming Zhong
Abstract:
This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method.
Keywords: Neural networks, Globally asymptotic stability, LMI approach, Additive time-varying delays.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 159545 Improved Stability Criteria for Neural Networks with Two Additive Time-Varying Delays
Authors: Miaomiao Yang, Shouming Zhong
Abstract:
This paper studies the problem of stability criteria for neural networks with two additive time-varying delays.A new Lyapunov-Krasovskii function is constructed and some new delay dependent stability criterias are derived in the terms of linear matrix inequalities(LMI), zero equalities and reciprocally convex approach.The several stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.
Keywords: Stability, Neural networks, Linear Matrix Inequalities (LMI) , Lyapunov function, Time-varying delays
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 147144 LMI Approach to Regularization and Stabilization of Linear Singular Systems: The Discrete-time Case
Authors: Salim Ibrir
Abstract:
Sufficient linear matrix inequalities (LMI) conditions for regularization of discrete-time singular systems are given. Then a new class of regularizing stabilizing controllers is discussed. The proposed controllers are the sum of predictive and memoryless state feedbacks. The predictive controller aims to regularizing the singular system while the memoryless state feedback is designed to stabilize the resulting regularized system. A systematic procedure is given to calculate the controller gains through linear matrix inequalities.
Keywords: Singular systems, Discrete-time systems, Regularization, LMIs
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 161443 Delay-Independent Closed-Loop Stabilization of Neutral System with Infinite Delays
Authors: I. Davies, O. L. C. Haas
Abstract:
In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.Keywords: Infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 279842 Asymptotic Stabilization of an Active Magnetic Bearing System using LMI-based Sliding Mode Control
Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd. Yatim
Abstract:
In this paper, stabilization of an Active Magnetic Bearing (AMB) system with varying rotor speed using Sliding Mode Control (SMC) technique is considered. The gyroscopic effect inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Also, transformation of the AMB dynamic model into a new class of uncertain system shows that this gyroscopic effect lies in the mismatched part of the system matrix. Moreover, the current gain parameter is allowed to be varied in a known bound as an uncertainty in the input matrix. SMC design method is proposed in which the sufficient condition that guarantees the global exponential stability of the reduced-order system is represented in Linear Matrix Inequality (LMI). Then, a new chattering-free control law is established such that the system states are driven to reach the switching surface and stay on it thereafter. The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.
Keywords: Active Magnetic Bearing (AMB), Sliding ModeControl (SMC), Linear Matrix Inequality (LMI), mismatcheduncertainty.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 155241 New Approaches on Stability Analysis for Neural Networks with Time-Varying Delay
Authors: Qingqing Wang, Shouming Zhong
Abstract:
Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.
Keywords: Neural networks, Globally asymptotic stability , LMI approach , IIA approach , Time-varying delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 196640 Sampling Effects on Secondary Voltage Control of Microgrids Based on Network of Multiagent
Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon
Abstract:
This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.Keywords: Microgrids, secondary control, multiagent, sampling, LMI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 148539 New Approaches on Exponential Stability Analysis for Neural Networks with Time-Varying Delays
Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong
Abstract:
In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dependent exponential stability criteria are established in terms of LMIs and can be easily checked.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.
Keywords: Neural networks, Exponential stability, LMI approach, Time-varying delays.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 209138 Takagi-Sugeno Fuzzy Control of Induction Motor
Authors: Allouche Moez, Souissi Mansour, Chaabane Mohamed, Mehdi Driss
Abstract:
This paper deals with the synthesis of fuzzy state feedback controller of induction motor with optimal performance. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate a non linear system in the synchronous d-q frame rotating with electromagnetic field-oriented. Next, a fuzzy controller is designed to stabilise the induction motor and guaranteed a minimum disturbance attenuation level for the closed-loop system. The gains of fuzzy control are obtained by solving a set of Linear Matrix Inequality (LMI). Finally, simulation results are given to demonstrate the controller-s effectiveness.
Keywords: Rejection disturbance, fuzzy modelling, open-loop control, Fuzzy feedback controller, fuzzy observer, Linear Matrix Inequality (LMI)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 193037 Exponential Stability of Uncertain Takagi-Sugeno Fuzzy Hopfield Neural Networks with Time Delays
Abstract:
In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. Finally, an example is given to illustrate our results by using MATLAB LMI toolbox.
Keywords: Hopfield neural network, linear matrix inequality, exponential stability, time delay, T-S fuzzy model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 153836 Delay-Dependent H∞ Performance Analysis for Markovian Jump Systems with Time-Varying Delays
Authors: Yucai Ding, Hong Zhu, Shouming Zhong, Yuping Zhang
Abstract:
This paper considers H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotical stability in mean square and a prescribed H∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed main results. All these results are expected to be of use in the study of stochastic systems with time-varying delays.
Keywords: H∞ performance, Markovian switching, Delaydependent stability, Linear matrix inequality (LMI)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 163735 H∞ Takagi-Sugeno Fuzzy State-Derivative Feedback Control Design for Nonlinear Dynamic Systems
Authors: N. Kaewpraek, W. Assawinchaichote
Abstract:
This paper considers an H∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H∞ TS fuzzy state-derivative feedback control law which guarantees L2-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.Keywords: H∞ fuzzy control, LMI, Takagi-Sugano (TS) fuzzy model, nonlinear dynamic systems, state-derivative feedback.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 97934 Speed Control of a Permanent Magnet Synchronous Machine (PMSM) Fed by an Inverter Voltage Fuzzy Control Approach
Authors: Jamel Khedri, Mohamed Chaabane, Mansour Souissi, Driss Mehdi
Abstract:
This paper deals with the synthesis of fuzzy controller applied to a permanent magnet synchronous machine (PMSM) with a guaranteed H∞ performance. To design this fuzzy controller, nonlinear model of the PMSM is approximated by Takagi-Sugeno fuzzy model (T-S fuzzy model), then the so-called parallel distributed compensation (PDC) is employed. Next, we derive the property of the H∞ norm. The latter is cast in terms of linear matrix inequalities (LMI-s) while minimizing the H∞ norm of the transfer function between the disturbance and the error ( ) ev T . The experimental and simulations results were conducted on a permanent magnet synchronous machine to illustrate the effects of the fuzzy modelling and the controller design via the PDC.Keywords: Feedback controller, Takagi-Sugeno fuzzy model, Linear Matrix Inequality (LMI), PMSM, H∞ performance.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 235933 An LMI Approach of Robust H∞ Fuzzy State-Feedback Controller Design for HIV/AIDS Infection System with Dual Drug Dosages
Authors: Wudhichai Assawinchaichote
Abstract:
This paper examines the problem of designing robust H controllers for for HIV/AIDS infection system with dual drug dosages described by a Takagi-Sugeno (S) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an H controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for the system. A sufficient condition of the controller for this system is given in term of Linear Matrix Inequalities (LMIs). The effectiveness of the proposed controller design methodology is finally demonstrated through simulation results. It has been shown that the anti-HIV vaccines are critically important in reducing the infected cells.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 182832 Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion
Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen
Abstract:
In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.
Keywords: Adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 209231 Robust Iterative PID Controller Based on Linear Matrix Inequality for a Sample Power System
Authors: Ahmed Bensenouci
Abstract:
This paper provides the design steps of a robust Linear Matrix Inequality (LMI) based iterative multivariable PID controller whose duty is to drive a sample power system that comprises a synchronous generator connected to a large network via a step-up transformer and a transmission line. The generator is equipped with two control-loops, namely, the speed/power (governor) and voltage (exciter). Both loops are lumped in one where the error in the terminal voltage and output active power represent the controller inputs and the generator-exciter voltage and governor-valve position represent its outputs. Multivariable PID is considered here because of its wide use in the industry, simple structure and easy implementation. It is also preferred in plants of higher order that cannot be reduced to lower ones. To improve its robustness to variation in the controlled variables, H∞-norm of the system transfer function is used. To show the effectiveness of the controller, divers tests, namely, step/tracking in the controlled variables, and variation in plant parameters, are applied. A comparative study between the proposed controller and a robust H∞ LMI-based output feedback is given by its robustness to disturbance rejection. From the simulation results, the iterative multivariable PID shows superiority.Keywords: Linear matrix inequality, power system, robust iterative PID, robust output feedback control
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 208230 ILMI Approach for Robust Output Feedback Control of Induction Machine
Authors: Abdelwahed Echchatbi, Adil Rizki, Ali Haddi, Nabil Mrani, Noureddine Elalami
Abstract:
In this note, the robust static output feedback stabilisation of an induction machine is addressed. The machine is described by a non homogenous bilinear model with structural uncertainties, and the feedback gain is computed via an iterative LMI (ILMI) algorithm.Keywords: Induction machine, Static output feedback, robust stabilisation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 190129 Exponential Passivity Criteria for BAM Neural Networks with Time-Varying Delays
Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong
Abstract:
In this paper,the exponential passivity criteria for BAM neural networks with time-varying delays is studied.By constructing new Lyapunov-Krasovskii functional and dividing the delay interval into multiple segments,a novel sufficient condition is established to guarantee the exponential stability of the considered system.Finally,a numerical example is provided to illustrate the usefulness of the proposed main results
Keywords: BAM neural networks, Exponential passivity, LMI approach, Time-varying delays.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 193928 Controlled Synchronization of an Array of Nonlinear System with Time Delays
Authors: S.M. Lee, J.H. Koo, J.H. Park, S.C. Won
Abstract:
In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.
Keywords: Synchronization, Delay, Lyapunov method, LMI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 146727 New Delay-dependent Stability Conditions for Neutral Systems with Nonlinear Perturbations
Authors: Lianglin Xiong, Xiuyong Ding, Shouming Zhong
Abstract:
In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.
Keywords: Asymptotical stability, neutral system, nonlinear perturbation, delay-dependent, linear matrix inequality (LMI).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 155326 Robust BIBO Stabilization Analysis for Discrete-time Uncertain System
Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye
Abstract:
The discrete-time uncertain system with time delay is investigated for bounded input bounded output (BIBO). By constructing an augmented Lyapunov function, three different sufficient conditions are established for BIBO stabilization. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Two numerical examples are provided to demonstrate the effectiveness of the derived results.
Keywords: Robust BIBO stabilization, delay-dependent stabilization, discrete-time system, time delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 161525 Stability of Interval Fractional-order Systems with Order 0 < α < 1
Authors: Hong Li, Shou-ming Zhong, Hou-biao Li
Abstract:
In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.
Keywords: Interval fractional-order systems, linear matrix inequality (LMI), asymptotical stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 364624 Leader-following Consensus Criterion for Multi-agent Systems with Probabilistic Self-delay
Authors: M.J. Park, K.H. Kim, O.M. Kwon
Abstract:
This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical example showed that the proposed method is effective.
Keywords: Multi-agent systems, probabilistic self-delay, consensus, Lyapunov method, LMI.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 177723 Robust Control for Discrete-Time Sector Bounded Systems with Time-Varying Delay
Authors: Ju H. Park, S.M. Lee
Abstract:
In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.
Keywords: Lur'e systems, Time-delay, Stabilization, LMIs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1709