Input-to-state stability for impulsive switched nonlinear systems with unstable subsystems

2017 ◽  
Vol 40 (7) ◽  
pp. 2167-2177 ◽  
Author(s):  
Meng Zhang ◽  
Lijun Gao
Keyword(s):  
Nonlinear Systems ◽  
Lower Bound ◽  
Lyapunov Function ◽  
Upper Bound ◽  
Switched Systems ◽  
Impulsive Effects ◽  
Switched Nonlinear Systems ◽  
Unstable Subsystems ◽  
Interval Approach ◽  
Impulsive Switched Systems

In this article, the input-to-state stability is investigated for impulsive switched systems. By means of the Lyapunov function and the average impulsive switched interval approach, the input-to-state stability properties are derived under the condition that all subsystems are stable, all subsystems are unstable and some subsystems are unstable. It is shown that if the continuous subsystems all have input-to-state stability and though the impulsive effects are destabilizing, the system has input-to-state stability with respect to a lower bound of the average impulsive switched interval. Moreover, if all the subsystems do not have input-to-state stability, the impulsive effects can still successfully stabilize the system but for an upper bound of the average impulsive switched interval. However, it is unveiled that if some continuous subsystems are not input-to-state stability, the impulsive effects can successfully stabilize the system for a lower bound of the average impulsive switched interval under specific conditions. It is worth noting that we introduce multiple jumps in this paper. Finally, three examples are illustrated with their simulations to manifest the validity of the main results.

Uniform Stability of Discrete-Time Switched Nonlinear Systems

2014 ◽  
Vol 643 ◽  
pp. 83-89
Author(s):  
Shu Rong Sun ◽  
Guang Rong Zhang ◽  
Ping Zhao
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Switched Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Uniform Stability ◽  
Switched Nonlinear Systems ◽  
Uniform Asymptotic Stability ◽  
Unstable Subsystems ◽  
The Stability

In this paper, we study the stability properties of a general class of nonautonomous discrete-time switched nonlinear systems. The switched systems consist of stable and unstable subsystems. Based on Lyapunov functions, some sufficient conditions for uniform stability, uniform asymptotic stability and uniform exponential stability are established.

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

2021 ◽  
pp. 107754632098598
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Multiple Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Common Lyapunov Function ◽  
Suggested Approach ◽  
Aggregation Techniques

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.

scholarly journals Exponential Stability for a Class of Switched Nonlinear Systems with Mixed Time-Varying Delays via an Average Dwell-Time Method

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
N. Yotha ◽  
T. Botmart ◽  
T. Mouktonglang
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Fast Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Time Varying Delay ◽  
Unstable Subsystems

The problem of exponential stability for a class of switched nonlinear systems with discrete and distributed time-varying delays is studied. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a fast time-varying function. We study the stability properties of switched nonlinear systems consisting of both stable and unstable subsystems. Average dwell-time approached and improved piecewise Lyapunov functional combined with Leibniz-Newton are formulated. New delay-dependent sufficient conditions for the exponential stabilization of the switched systems are first established in terms of LMIs. A numerical example is also given to illustrate the effectiveness of the proposed method.

Tracking Control for Switched Nonlinear Systems Subject to Time-Varying Output Constraints

2012 ◽  
Author(s):  
Ben Niu ◽  
Georgi M. Dimirovski ◽  
Jun Zhao
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Tracking Control ◽  
Closed Loop ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Feedback Form ◽  
Barrier Lyapunov Function ◽  
Output Constraints ◽  
Asymptotic Tracking

In this paper, we address the tracking control problem for switched nonlinear systems in strict-feedback form with time-varying output constraints. To prevent the output from violating the time-varying constraints, we employ a Barrier Lyapunov Function, which relies explicitly on time. Based on the simultaneous domination assumption, we design a controller for the switched system, which guarantees that asymptotic tracking is achieved without transgression of the constraints and all closed-loop signals remain bounded under arbitrary switchings. The effectiveness of the proposed results is illustrated using a numerical example.

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.

Sign in / Sign up

Export Citation Format

Share Document