Search results for: Linear matrix inequality

Authors: Wookyong Kwon, Sangmoon Lee

Abstract:

In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: Model predictive control, sampled-data control, linear parameter varying systems, LPV.

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Authors: Sung Wook Yun, Yun Jong Choi, Kyong-min Lee, Poogyeon Park*

Abstract:

Repetitive systems stand for a kind of systems that perform a simple task on a fixed pattern repetitively, which are widely spread in industrial fields. Hence, many researchers have been interested in those systems, especially in the field of iterative learning control (ILC). In this paper, we propose a finite-horizon tracking control scheme for linear time-varying repetitive systems with uncertain initial conditions. The scheme is derived both analytically and numerically for state-feedback systems and only numerically for output-feedback systems. Then, it is extended to stable systems with input constraints. All numerical schemes are developed in the forms of linear matrix inequalities (LMIs). A distinguished feature of the proposed scheme from the existing iterative learning control is that the scheme guarantees the tracking performance exactly even under uncertain initial conditions. The simulation results demonstrate the good performance of the proposed scheme.

Keywords: Finite time horizon, linear matrix inequality (LMI), repetitive system, uncertain initial condition.

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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.

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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.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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Authors: J. Cheeneebash, V. Beeharry, A. Gopaul

Abstract:

The aim of this paper is to express the input-output matrix as a linear ordering problem which is classified as an NP-hard problem. We then use a Tabu search algorithm to find the best permutation among sectors in the input-output matrix that will give an optimal solution. This optimal permutation can be useful in designing policies and strategies for economists and government in their goal of maximizing the gross domestic product.

Keywords: Input-Output matrix, linear ordering problem, Tabusearch.

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Authors: J. P. P. Andrade, V. A. F. Campos

Abstract:

This work presents an application of Linear Matrix Inequalities (LMI) for the robust control of an F-16 aircraft through an algorithm ensuring the damping factor to the closed loop system. The results show that the zero and gain settings are sufficient to ensure robust performance and stability with respect to various operating points. The technique used is the pole placement, which aims to put the system in closed loop poles in a specific region of the complex plane. Test results using a dynamic model of the F-16 aircraft are presented and discussed.

Keywords: F-16 Aircraft, linear matrix inequalities, pole placement, robust control.

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Authors: S. H. Nasseri, M. Sohrabi, E. Ardil

Abstract:

In this paper, we give a certain decomposition of the coefficient matrix of the fully fuzzy linear system (FFLS) to obtain a simple algorithm for solving these systems. The new algorithm can solve FFLS in a smaller computing process. We will illustrate our method by solving some examples.

Keywords: Fully fuzzy linear system, Fuzzy number, LUdecomposition.

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Authors: Ejaz Khan, Conor Heneghan

Abstract:

In this paper we propose a new criterion for solving the problem of channel shortening in multi-carrier systems. In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Minimum mean square error (MMSE) method for TEQ does not give satisfactory results. In [1] a new criterion for partially equalizing severe ISI channels to reduce the cyclic prefix overhead of the discrete multitone transceiver (DMT), assuming a fixed transmission bandwidth, is introduced. Due to specific constrained (unit morm constraint on the target impulse response (TIR)) in their method, the freedom to choose optimum vector (TIR) is reduced. Better results can be obtained by avoiding the unit norm constraint on the target impulse response (TIR). In this paper we change the cost function proposed in [1] to the cost function of determining the maximum of a determinant subject to linear matrix inequality (LMI) and quadratic constraint and solve the resulting optimization problem. Usefulness of the proposed method is shown with the help of simulations.

Keywords: Equalizer, target impulse response, convex optimization, matrix inequality.

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Authors: Tomoaki Hashimoto

Abstract:

Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the effectiveness of the obtained stability condition.

Keywords: Computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems.

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Authors: Nicholas D. Assimakis

Abstract:

In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: Discrete time, linear estimation, Kalman filter, Kalman filter gain.

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Authors: Milan Hladik

Abstract:

The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

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Authors: Zhong-xi Gao, Hou-biao Li

Abstract:

Recently, some convergent results of the generalized AOR iterative (GAOR) method for solving linear systems with strictly diagonally dominant matrices are presented in [Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant cofficient matrices. Appl. Math. Comput. 176, 128-133 (2006)] and [Tian, G.X., Huang, T.Z., Cui, S.Y.: Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant cofficient matrices. J. Comp. Appl. Math. 213, 240-247 (2008)]. In this paper, we give the convergence of the GAOR method for linear systems with strictly doubly diagonally dominant matrix, which improves these corresponding results.

Keywords: Diagonally dominant matrix, GAOR method, Linear system, Convergence

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Authors: Mengzhuo Luo, Shouming Zhong

Abstract:

This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived.

Keywords: Delay-dependent stability, Neural networks, Time varying delay, Linear matrix inequality (LMI).

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Authors: Shoji Katagiri

Abstract:

This paper is to clarify the relationship between ICT and income inequality. To do so, we develop the general equilibrium model with ICT investment, obtain the equilibrium solutions, and then simulate the model with these solutions for some OECD countries. As a result, generally, during the corresponding periods we confirm that the relationship between ICT investment and income inequality is positive. In this mode, the increment of the ratio of ICT investment to the aggregated investment in stock enhances the capital’s share of income, and finally leads to income inequality such as the increase of the share of the top decile income. Although we confirm the positive relationship between ICT investment and income inequality, the upward trend for that relationship depends on the values of parameters for the making use of the simulations and these parameters are not deterministic in the magnitudes on the calculated results for the simulations.

Keywords: ICT, inequality, capital accumulation, technology.

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Authors: Kelong Zheng, Shouming Zhong

Abstract:

A new nonlinear sum-difference inequality in two variables which generalize some existing results and can be used as handy tools in the analysis of certain partial difference equation is discussed. An example to show boundedness of solutions of a difference value problem is also given.

Keywords: Sum-Difference inequality, Nonlinear, Boundedness.

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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.

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Authors: Lili Wang

Abstract:

By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and  effectiveness of the results.

Keywords: Almost periodic solution, Exponential stability, Neural networks, Impulses.

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Authors: F. Khaber, K. Zehar, A. Hamzaoui

Abstract:

In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.

Keywords: Takagi-Sugeno fuzzy model, state feedback, linear matrix inequalities, robust stability.

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Authors: Min Sun, Jing Liu

Abstract:

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point ˜xk, and then the multiplier yk is updated to get the new iterate yk+1. In order to get xk+1, we adopt a new descent direction which is simple compared with the existing prediction-correction type ADMs. For the inexact ADM, the resulting proximal subproblem has closedform solution when the proximal parameter and inexact term are chosen appropriately. We show the efficiency of the inexact ADM numerically by some preliminary numerical experiments.

Keywords: variational inequality problems, alternating direction method, global convergence

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Authors: Shoji Katagiri

Abstract:

This study deals with wage inequality in organization and shows the relationship between ICT and wage in organization. To do so, we incorporate ICT’s factors in organization into our model. ICT’s factors are efficiencies of Enterprise Resource Planning (ERP), Computer Assisted Design/Computer Assisted Manufacturing (CAD/CAM), and NETWORK. The improvement of ICT’s factors decrease the learning cost to solve problem pertaining to the hierarchy in organization. The improvement of NETWORK increases the wage inequality within workers and decreases within managers and entrepreneurs. The improvements of CAD/CAM and ERP increases the wage inequality within all agent, and partially increase it between the agents in hierarchy.

Keywords: Endogenous economic growth, ICT, inequality, capital accumulation, technology.

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Authors: Ghazi S. Kahmmash

Abstract:

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

Keywords: Generating functions, Recurrences relation and Generalization of the new class matrix polynomial set.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of asymptotically stability for neural networks with time-varying delays.By establishing a suitable Lyapunov-Krasovskii function and several novel sufficient conditions are obtained to guarantee the asymptotically stability of the considered system. Finally,two numerical examples are given to illustrate the effectiveness of the proposed main results.

Keywords: Neural networks, Lyapunov-Krasovskii, Time-varying delays, Linear matrix inequality.

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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

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Authors: A. K. Al-Othman

Abstract:

This study presents a new approach based on Tanaka's fuzzy linear regression (FLP) algorithm to solve well-known power system economic load dispatch problem (ELD). Tanaka's fuzzy linear regression (FLP) formulation will be employed to compute the optimal solution of optimization problem after linearization. The unknowns are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the unknowns. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the unknowns, subject to double inequality constraints. Linear programming technique is employed to obtain the middle and the symmetric spread for every unknown (power generation level). Simulation results of the proposed approach will be compared with those reported in literature.

Keywords: Economic Dispatch, Fuzzy Linear Regression (FLP)and Optimization.

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Authors: C. Ardil

Abstract:

This paper introduces a new method for multiplecriteria decision making (MCDM) that avoids order reversal and ensures consistency in decision-making. The proposed method involves range targeting of benefit and cost criteria vectors for range normalization of the initial decision matrix. The Reference Linear Combination (RLC) is used to avoid the rank reversal problem. The preference order generated from the target score matrix does not require relative comparisons between alternatives but relies on a chosen reference solution point after transforming the original decision matrix into an MCDM problem by specifying the minimum and maximum bounds of each criterion. The efficiency and applicability of the proposed RLC method were demonstrated in the selection of commercial passenger aircraft. 

Keywords: Aircraft selection, reference linear combination (RLC), multiple criteria decision-making, MCDM

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Authors: Azita Tajaddini, Ramleh Shamsi

Abstract:

In this paper, we present the block generalized minimal residual (BGMRES) method in order to solve the generalized Sylvester matrix equation. However, this method may not be converged in some problems. We construct a polynomial preconditioner based on BGMRES which shows why polynomial preconditioner is superior to some block solvers. Finally, numerical experiments report the effectiveness of this method.

Keywords: Linear matrix equation, Block GMRES, matrix Krylov subspace, polynomial preconditioner.

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Authors: Biao Qin, Jin Huang, Jiaojiao Ren, Wei Kang

Abstract:

This paper deals with the problem of passivity analysis for stochastic neural networks with leakage, discrete and distributed delays. By using delay partitioning technique, free weighting matrix method and stochastic analysis technique, several sufficient conditions for the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), in which both the time-delay and its time derivative can be fully considered. A numerical example is given to show the usefulness and effectiveness of the obtained results.

Keywords: Passivity, Stochastic neural networks, Multiple time delays, Linear matrix inequalities (LMIs).

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Authors: Jiann-Ming Wu, Hsiao-Chang Chen, Chun-Chang Wu, Pei-Hsun Hsu

Abstract:

This work explores blind image deconvolution by recursive function approximation based on supervised learning of neural networks, under the assumption that a degraded image is linear convolution of an original source image through a linear shift-invariant (LSI) blurring matrix. Supervised learning of neural networks of radial basis functions (RBF) is employed to construct an embedded recursive function within a blurring image, try to extract non-deterministic component of an original source image, and use them to estimate hyper parameters of a linear image degradation model. Based on the estimated blurring matrix, reconstruction of an original source image from a blurred image is further resolved by an annealed Hopfield neural network. By numerical simulations, the proposed novel method is shown effective for faithful estimation of an unknown blurring matrix and restoration of an original source image.

Keywords: Blind image deconvolution, linear shift-invariant(LSI), linear image degradation model, radial basis functions (rbf), recursive function, annealed Hopfield neural networks.

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