Exponential stability for switched delay systems based on average dwell time technique and Lyapunov function method

2006 ◽  
Author(s):  
Xi-Ming Sun ◽  
G.M. Dimirovski ◽  
Jun Zhao ◽  
Wei Wang
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Dwell Time ◽  
Function Method ◽  
Average Dwell Time ◽  
Delay Systems ◽  
Lyapunov Function Method

Stability and L2–Gain analysis of linear switched singular systems by using multiple discontinuous Lyapunov function approach

2019 ◽  
Vol 41 (15) ◽  
pp. 4197-4206 ◽  
Author(s):  
Jumei Wei ◽  
Huimin Zhi ◽  
Kai Liu
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Discrete Time ◽  
Text Analysis ◽  
Dwell Time ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Function Approach ◽  
Discrete Time Case

In this paper, the problem of the E-exponential stability and [Formula: see text] analysis of linear switched singular systems is investigated in discrete-time case. By using a multiple discontinuous Lyapunov function approach and adopting the mode-dependent average dwell time (MDADT) switching signals, new sufficient conditions of E-exponential stability and [Formula: see text] analysis for linear switched singular systems are presented. Based on the above results, we also derive the weighted [Formula: see text] performance index. In addition, by utilizing our proposed method, tighter bounds on average dwell time can be obtained for our considered systems. At last, a numerical example is given to show the effectiveness of the results.

scholarly journals Robust Stability of Switched Delay Systems with Average Dwell Time under Asynchronous Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Jun Cheng ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang
Keyword(s):  
Exponential Stability ◽  
Robust Stability ◽  
Integral Inequality ◽  
Global Exponential Stability ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Delay Systems ◽  
Asynchronous Switching ◽  
Average Dwell Time Method

The problem of robust stability of switched delay systems with average dwell time under asynchronous switching is investigated. By taking advantage of the average dwell-time method and an integral inequality, two sufficient conditions are developed to guarantee the global exponential stability of the considered switched system. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques.

scholarly journals Delay-Dependent Stability Analysis for Uncertain Switched Time-Delay Systems Using Average Dwell Time

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yangming Zhang ◽  
Peng Yan
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Exponential Stability ◽  
Switched Systems ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Delay System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Delay Dependent

We are concerned with the stability problem for linear discrete-time switched systems with time delays. The problem is solved by using multiple Lyapunov functions to develop constructive tools for the exponential stability analysis of the switched time-delay system. Furthermore, the uncertainties of the switched systems are also taken into consideration. Sufficient delay-dependent conditions are derived in terms of the average dwell time for the exponential stability based on linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

scholarly journals The Method of Lyapunov Function and Exponential Stability of Impulsive Delay Systems with Delayed Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Pei Cheng ◽  
Feiqi Deng ◽  
Lianglong Wang
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Impulsive Systems ◽  
Lyapunov Function Method ◽  
Impulsive Delay ◽  
Delayed Impulses

This paper investigates the exponential stability of general impulsive delay systems with delayed impulses. By using the Lyapunov function method, some Lyapunov-based sufficient conditions for exponential stability are derived, which are more convenient to be applied than those Razumikhin-type conditions in the literature. Their applications to linear impulsive systems with time-varying delays are also proposed, and a set of sufficient conditions for exponential stability is provided in terms of matrix inequalities. Meanwhile, two examples are discussed to illustrate the effectiveness and advantages of the results obtained.

scholarly journals Pinning Synchronization of Switched Complex Dynamical Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Liming Du ◽  
Feng Qiao ◽  
Fengying Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Function Method ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Dynamical Networks ◽  
Switching Law ◽  
Arbitrary Switching ◽  
Lyapunov Function Method ◽  
Networks With Switching Topology

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

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