scholarly journals ISS and integral-ISS of switched systems with nonlinear supply functions

2021 ◽  
Author(s):  
Shenyu Liu ◽  
Aneel Tanwani ◽  
Daniel Liberzon
Keyword(s):  
Switched Systems ◽  
Lyapunov Functions ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Switched Nonlinear Systems ◽  
Activation Time ◽  
Unstable Subsystems ◽  
Supply Functions ◽  
Dissipation Inequalities ◽  
Integral Version

AbstractThe problem of input-to-state stability (ISS) and its integral version (iISS) are considered for switched nonlinear systems with inputs, resets and possibly unstable subsystems. For the dissipation inequalities associated with the Lyapunov function of each subsystem, it is assumed that the supply functions, which characterize the decay rate and ISS/iISS gains of the subsystems, are nonlinear. The change in the value of Lyapunov functions at switching instants is described by a sum of growth and gain functions, which are also nonlinear. Using the notion of average dwell-time (ADT) to limit the number of switching instants on an interval, and the notion of average activation time (AAT) to limit the activation time for unstable systems, a formula relating ADT and AAT is derived to guarantee ISS/iISS of the switched system. Case studies of switched systems with saturating dynamics and switched bilinear systems are included for illustration of the results.

scholarly journals Stability Analysis of a Class of Switched Nonlinear Systems with an Improved Average Dwell Time Method

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Rongwei Guo
Keyword(s):  
Stability Analysis ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Asymptotically Stable ◽  
Switched Nonlinear Systems ◽  
Globally Asymptotically Stable ◽  
Unstable Subsystems ◽  
Average Dwell Time Method ◽  
The Stability

This paper investigates the stability of switched nonlinear (SN) systems in two cases: (1) all subsystems are globally asymptotically stable (GAS), and (2) both GAS subsystems and unstable subsystems coexist, and it proposes a number of new results on the stability analysis. Firstly, an improved average dwell time (ADT) method is presented for the stability of such switched system by extending our previous dwell time method. In particular, an improved mode-dependent average dwell time (MDADT) method for the switched systems whose subsystems are quadratically stable (QS) is also obtained. Secondly, based on the improved ADT and MDADT methods, several new results to the stability analysis are obtained. It should be pointed out that the obtained results have two advantages over the existing ones; one is that the improved ADT method simplifies the conditions of the existing ADT method, the other is that the obtained lower bound of ADT (τa*) is also smaller than that obtained by other methods. Finally, illustrative examples are given to show the correctness and the effectiveness of the proposed methods.

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.

PIECEWISE LYAPUNOV FUNCTIONS FOR SWITCHED SYSTEMS WITH AVERAGE DWELL TIME

2008 ◽  
Vol 2 (3) ◽  
pp. 192-197 ◽  
Author(s):  
Guisheng Zhai ◽  
Bo Hu ◽  
Kazunori Yasuda ◽  
Anthony N. Michel
Keyword(s):  
Switched Systems ◽  
Lyapunov Functions ◽  
Dwell Time ◽  
Average Dwell Time

scholarly journals Stability Analysis of Fractional Switched Systems With Stable and Unstable Subsystems

2021 ◽  
Author(s):  
Ran Yang ◽  
Song Liu ◽  
Xiaoyan Li ◽  
Jian Xiao
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Stability Conditions ◽  
Razumikhin Technique ◽  
Unstable Subsystems ◽  
Slow Switching

Abstract This article addresses stability of fractional switched systems (FSSs) with stable and unstable subsystems. First, several algebraic conditions are presented to guarantee asymptotic stability by applying multiple Lyapunov function (MLF) method, dwell time technique and fast-slow switching mechanism. Then, some stability conditions which have less conservation are also provided by utilizing average dwell time (ADT) technique and the property of Mittag-Leffler function. In addition, sufficient conditions on asymptotic stability of delayed FSSs are obtained by virtue of fractional Razumikhin technique. Finally, several examples are given to reveal that the conclusions obtained are valid.

scholarly journals Stability of switched systems with admissible switching signals

2021 ◽  
Author(s):  
Hui-Ting Wang ◽  
Yong He ◽  
Qing-Guo Wang ◽  
Chuan-Ke Zhang ◽  
Min Wu
Keyword(s):  
Nonlinear Systems ◽  
Stability Condition ◽  
Switched Systems ◽  
Dwell Time ◽  
Divergence Time ◽  
Average Dwell Time ◽  
Sufficient Condition ◽  
Switched Nonlinear Systems ◽  
Equal Compensation ◽  
Stability Results

Abstract In this paper, stability of switched systems is investigated for a class of switching signals which meet some admissibility conditions. Firstly, the admissible edge-dependent divergence time is defined in terms of admissible transition edges and it will vary with the compensation bounds. Then the admissible edge-dependent bounded maximum average dwell time (BMADT) is imposed on switching signals. As a result, a sufficient condition is obtained for globally uniformly exponential stability of switched nonlinear systems with such switching signals. Secondly, by setting the equal compensation bounds for the same reaching subsystems, the mode-dependent divergence time is defined, and then the mode-dependent BMADT is proposed. A stability condition under the mode-dependent BMADT is established. These stability results are then applied to switched linear systems. The numerical example is presented to show that the proposed techniques are less restrictive and more flexible in application, compared with the BMADT.

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