scholarly journals Robust Observer Design for Switched Positive Linear System with Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanke Zhong ◽  
Tefang Chen
Keyword(s):  
Linear System ◽  
Linear Matrix Inequality ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Robust Observer ◽  
Slack Variable

This paper is concerned with the design of a robust observer for the switched positive linear system with uncertainties. Sufficient conditions of building a robust observer are established by using the multiple copositive Lyapunov-krasovskii function and the average dwell time approach. By introducing an auxiliary slack variable, these sufficient conditions are transformed into LMI (linear matrix inequality). A numerical example is given to illustrate the validities of obtained results.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

Robust adaptive state estimation for uncertain nonlinear switched systems with unknown inputs

2016 ◽  
Vol 40 (4) ◽  
pp. 1082-1091 ◽  
Author(s):  
Junqi Yang ◽  
Yantao Chen ◽  
Zheng Zheng ◽  
Wei Qian
Keyword(s):  
State Estimation ◽  
Switched Systems ◽  
Dwell Time ◽  
Sliding Mode ◽  
Lipschitz Constant ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Nonlinear Switched Systems ◽  
Continuous State

This paper discusses the issue of the continuous state estimation for a class of uncertain nonlinear switched systems under the two cases of both average dwell time and mode-dependent average dwell time. A robust and adaptive switched observer is developed such that the states of an original nonlinear switched system can be asymptotically estimated, where the Lipschitz constant of the nonlinear term may be unknown since the designed adaptation law can adaptively adjust it. Based on the feasible solution of an optimization problem with a linear matrix inequality constraint, the observer gain matrices are obtained and guarantee the existence of a robust switched observer. Meanwhile, the switching signals are designed such that the observer error dynamics is globally uniformly exponentially stable, and the sufficient conditions of the existence of a robust sliding-mode switched observer are derived. Finally, the effectiveness of the proposed approaches is illustrated by a numerical example and switched Rössler chaotic dynamics.

STABILITY ANALYSIS FOR DELAYED CELLULAR NEURAL NETWORKS BASED ON LINEAR MATRIX INEQUALITY APPROACH

2004 ◽  
Vol 14 (09) ◽  
pp. 3377-3384 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
SHIZHONG YANG
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach ◽  
Functional Differential ◽  
The Stability

Some sufficient conditions for the asymptotic stability of cellular neural networks with time delay are derived using the Lyapunov–Krasovskii stability theory for functional differential equations as well as the linear matrix inequality (LMI) approach. The analysis shows how some well-known results can be refined and generalized in a straightforward manner. Moreover, the stability criteria obtained are delay-independent. They are less conservative and restrictive than those reported so far in the literature, and provide a more general set of criteria for determining the stability of delayed cellular neural networks.

Ultimate Boundedness of Stochastic Neural Networks with Delays

2011 ◽  
Vol 204-210 ◽  
pp. 1549-1552
Author(s):  
Li Wan ◽  
Qing Hua Zhou
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Lyapunov Functional ◽  
Signal Transmission ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequality ◽  
Ultimate Boundedness

Although ultimate boundedness of several classes of neural networks with constant delays was studied by some researchers, the inherent randomness associated with signal transmission was not taken account into these networks. At present, few authors study ultimate boundedness of stochastic neural networks and no related papers are reported. In this paper, by using Lyapunov functional and linear matrix inequality, some sufficient conditions ensuring the ultimate boundedness of stochastic neural networks with time-varying delays are established. Our criteria are easily tested by Matlab LMI Toolbox. One example is given to demonstrate our criteria.

A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs

2020 ◽  
Author(s):  
Roya Karimi ◽  
Jianqiang Cheng ◽  
Miguel A. Lejeune
Keyword(s):  
Linear Matrix Inequality ◽  
Numerical Study ◽  
Sufficient Conditions ◽  
Sample Average Approximation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Convex Approximation ◽  
Sample Average ◽  
Algorithmic Framework ◽  
Average Approximation

We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology matrix and CCLMI with random right-hand side. We propose a series of computationally tractable PSAA-based approximations for CCLMI problems, analyze their properties, and derive sufficient conditions that ensure convexity for the two most popular—normal and uniform—continuous distributions. We derive several semidefinite programming PSAA reformulations efficiently solved by off-the-shelf solvers and design a sequential convex approximation method for the PSAA formulations containing bilinear matrix inequalities. The proposed methods can be generalized to other continuous random variables whose cumulative distribution function can be easily computed. We carry out a comprehensive numerical study on three practical CCLMI problems: robust truss topology design, calibration, and robust control. The tests attest to the superiority of the PSAA reformulation and algorithmic framework over the scenario and sample average approximation methods. Summary of Contribution: In line with the mission and scope of IJOC, we study an important type of optimization problems, chance-constrained linear matrix inequality (CCLMI) problems, which require stochastic linear matrix inequality (LMI) constraints to be satisfied with high probability. To solve CCLMI problems, we propose a novel partial sample average approximation (PSAA) framework: (i) develop a series of computationally tractable PSAA-based approximations for CCLMI problems, (ii) analyze their properties, (iii) derive sufficient conditions ensuring convexity, and (iv) design a sequential convex approximation method. We evaluate our proposed method via a comprehensive numerical study on three practical CCLMI problems. The tests attest the superiority of the PSAA reformulation and algorithmic framework over standard benchmarks.

Reduced-Order Observer Design for Discrete-Time Descriptor Systems With Unknown Inputs: An Linear Matrix Inequality Approach

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Shenghui Guo ◽  
Fanglai Zhu
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Observer Design ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Unknown Input ◽  
Matrix Inequality ◽  
Reduced Order ◽  
Unknown Inputs ◽  
Reduced Order Observer

Reduced-order observer design methods for both linear and nonlinear discrete-time descriptor systems based on the linear matrix inequality (LMI) approach are investigated. We conclude that the conditions under which a full-order observer exists can also guarantee the existence of a reduced-order observer. By choosing a special reduced-order observer gain matrix, a reduced-order unknown input observer is proposed for linear system with unknown inputs, and then an unknown input reconstruction is provided for some special cases. We also extend above results to the cases of nonlinear systems. Finally, three numerical comparative simulation examples are given to illustrate the effectiveness and merits of proposed methods.

scholarly journals Robust Exponential Stabilization for a Class of Nonlinear Uncertain Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 312-319
Author(s):  
Meng Liu ◽  
Yali Dong ◽  
Xinyue Tang
Keyword(s):  
Linear Matrix Inequality ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Exponential Stabilization ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Robust Exponential Stabilization ◽  
Nonlinear Uncertain Systems

This paper is concerned with the problem of robust exponential stabilization for a class of nonlinear uncertain systems with time-varying delays. By using appropriately chosen Lyapunov-Krasovskii functional, together with the Finsler’s lemma, sufficient conditions for exponential stability of nonlinear uncertain systems with time-varying delays are proposed in terms of linear matrix inequality (LMI). Then, novel sufficient conditions are developed to ensure the nonlinear uncertain system with time-varying delay is robust exponentially stabilizable in terms of linear matrix inequality with state feedback control. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

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