scholarly journals Robust stability of impulsive switched systems with disturbance

2006 ◽  
Vol 48 (2) ◽  
pp. 259-270
Author(s):  
Xinzhi Liu ◽  
Hongtao Zhang
Keyword(s):  
Switched Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Simple Approach ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Multiple Lyapunov Functions ◽  
Impulsive Switched Systems ◽  
Bounded Disturbance

AbstractThis paper studies a class of impulsive switched systems with persistent bounded disturbance using robust attractor analysis and multiple Lyapunov functions. Some sufficient conditions for internal stability of the systems are obtained in terms of linear matrix inequalities (LMI). Based on the results, a simple approach for the design of a feedback controller is presented to achieve a desired level of disturbance attenuation. Numerical examples are also worked out to illustrate the obtained results.

Global dissipativity of stochastic Lotka–Volterra system with feedback controls

2017 ◽  
Vol 10 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Qimin Zhang ◽  
Xinjing Zhang ◽  
Hongfu Yang
Keyword(s):  
Linear Matrix Inequalities ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Volterra System ◽  
Feedback Controls ◽  
The Mean

In this paper, a class of stochastic Lotka–Volterra system with feedback controls is considered. The purpose is to establish some criteria to ensure the system is globally dissipative in the mean square. By constructing suitable Lyapunov functions as well as combining with Jensen inequality and It[Formula: see text] formula, the sufficient conditions are established and they are expressed in terms of the feasibility to a couple linear matrix inequalities (LMIs). Finally, the main results are illustrated by examples.

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Disturbance Attenuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Switched State Feedback

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

scholarly journals Robust Finite-TimeH∞Control for Impulsive Switched Nonlinear Systems with State Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jian Guo ◽  
Chao Liu ◽  
Zhengrong Xiang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Switched Nonlinear Systems ◽  
State Delay ◽  
Impulsive Switched Systems ◽  
Finite Time Boundedness ◽  
Impulsive Switched System

This paper investigates robust finite-timeH∞control for a class of impulsive switched nonlinear systems with time-delay. Firstly, using piecewise Lyapunov function, sufficient conditions ensuring finite-time boundedness of the impulsive switched system are derived. Then, finite-timeH∞performance analysis for impulsive switched systems is developed, and a robust finite-timeH∞state feedback controller is proposed to guarantee that the resulting closed-loop system is finite-time bounded withH∞disturbance attenuation. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method.

Stability of a class of nonlinear fractional order impulsive switched systems

2016 ◽  
Vol 39 (5) ◽  
pp. 781-790 ◽  
Author(s):  
Guopei Chen ◽  
Ying Yang
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Multiple Lyapunov Functions ◽  
Unstable Subsystems ◽  
Impulsive Switched Systems ◽  
The Stability ◽  
Work First ◽  
Periodic Switching

This paper considers the asymptotic stability of a class of nonlinear fractional order impulsive switched systems by extending the result of existing work. First, a criterion is given to verify the stability of systems by using the Mittag–Leffler function and fractional order multiple Lyapunov functions. Second, by combining the methods of minimum dwell time with fractional order multiple Lyapunov functions, another sufficient condition for the stability of systems is given. Third, by using a periodic switching technique, a switching signal is designed to ensure the asymptotic stability of a system with both stable and unstable subsystems. Finally, two numerical examples are provided to illustrate the theoretical results.

scholarly journals Fault Detection for Discrete-Time Nonlinear Impulsive Switched Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Qingyu Su ◽  
Xiaolong Jia ◽  
Zhengfan Song
Keyword(s):  
Fault Detection ◽  
Discrete Time ◽  
Switched Systems ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Robust Performance ◽  
Detection Problem ◽  
Convex Optimization Problem ◽  
Impulsive Switched Systems

This paper investigates the fault detection problem for discrete-time nonlinear impulsive switched systems. Attention is focused on designing the fault detection filters to guarantee the robust performance and the detection performance. Based on these performances, sufficient conditions for the existence of filters are given in the framework of linear matrix inequality; furthermore, the filter gains are characterized by a convex optimization problem. The presented technique is validated by an example. Simulation results indicate that the proposed method can effectively detect the faults.

H ∞ Guaranteed Cost Filtering for Uncertain Discrete-Time Switched Systems With Multiple Time-Varying Delays

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Haibin Sun ◽  
Guangdeng Zong ◽  
Linlin Hou
Keyword(s):  
Discrete Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Guaranteed Cost ◽  
The Cost

This paper deals with the problem of H∞ guaranteed cost filtering for uncertain discrete-time switched systems with multiple time-varying delays. The switched system under consideration is subject to time-varying norm-bounded parameter uncertainties in all the system matrices. The aim is to design a filter, which guarantees the asymptotical stability of the error system with prescribed disturbance attenuation for all admissible uncertainties and the cost function value is not more than a specified upper bound. By resorting to a switched Lyapunov function, some delay-dependent sufficient conditions are presented in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed algorithms.

Asynchronous H∞ filtering fault detection for discrete-time switched linear systems

2021 ◽  
pp. 014233122110320
Author(s):  
Jinjie Huang ◽  
Xianzhi Hao ◽  
Xiaozhen Pan
Keyword(s):  
Fault Detection ◽  
Linear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Evaluation System ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Switched Linear Systems

This article studies the asynchronous H∞ filtering fault detection for discrete-time switched linear systems with mode-dependent average dwell time (MDADT). Firstly, a series of mode-dependent fault detection filters are designed, and augmented with original switched systems to construct a residual evaluation system. However, in practice, the switching of the filter often lags behind the corresponding subsystem. To deal with this, the running time of the subsystem is divided into two parts: the matched and the mismatched. Then the asynchronous switched residual evaluation system is obtained, and global uniform exponential stability (GUES) and exponential H∞ performance of asynchronous switched system are guaranteed by using μ-dependent discontinuous multi-Lyapunov functions and MDADT method. The sufficient conditions for the existence of designed filter are given in terms of linear matrix inequalities (LMIs), and parameter matrices of the designed filter and MDADT can be obtained by solving these LMIs. Finally, the effectiveness of the proposed method is demonstrated by two examples.

Generalized non-monotonic Lyapunov functions for analysis and synthesis of Takagi-Sugeno fuzzy systems

2020 ◽  
Vol 39 (3) ◽  
pp. 4147-4158
Author(s):  
Pedro H.S. Coutinho ◽  
Márcia L.C. Peixoto ◽  
Márcio J. Lacerda ◽  
Miguel Bernal ◽  
Reinaldo M. Palhares
Keyword(s):  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
State Of The Art ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Current State ◽  
Quadratic Lyapunov Functions ◽  
Analysis And Synthesis ◽  
Takagi Sugeno

This paper presents new stability and stabilisation conditions in the form of linear matrix inequalities for discrete-time Takagi-Sugeno fuzzy systems; they are derived considering a class of non-quadratic Lyapunov functions with multi-parametric non-monotonic terms, which significantly enhances the feasibility set of current state-of-the-art results. In addition, extensions to cope with the disturbance attenuation control problem are included. Benchmark numerical examples are provided to illustrate the effectiveness of the proposed approach.

scholarly journals Almost Global Stability of Nonlinear Switched Systems with Time-Dependent Switching

2018 ◽  
Author(s):  
Ozkan Karabacak ◽  
Aysegul Kivilcim ◽  
Rafael Wisniewski
Keyword(s):  
Global Stability ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Dwell Time ◽  
Autonomous Systems ◽  
Sufficient Conditions ◽  
Multiple Lyapunov Functions ◽  
Koopman Operator ◽  
Nonlinear Switched Systems

For a dynamical system, it is known that the existence of a Lyapunov density implies almost global stability of an equilibrium. It is then natural to ask whether the existence of a common Lyapunov density for a nonlinear switched system implies almost global stability, in the same way as a common Lyapunov function implies global stability for nonlinear switched systems. In this work, the answer to this question is shown to be affirmative as long as switchings satisfy a dwell-time constraint with an arbitrarily small dwell time. As a straightforward extension of this result, we employ multiple Lyapunov densities in analogy with the role of multiple Lyapunov functions for the global stability of switched systems. This gives rise to a minimum dwell time estimate to ensure almost global stability of nonlinear switched systems, when a common Lyapunov density does not exist. The results obtained for continuous-time switched systems are based on some sufficient conditions for the almost global stability of discrete-time non-autonomous systems. These conditions are obtained using the duality between Frobenius-Perron operator and Koopman operator.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

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