Paper Info
Title
Improved stability results for discrete-time switched systems: A multiple piecewise convex Lyapunov function approach.
Abstract
In this paper, the stability problem is investigated for a class of discrete-time switched systems with unstable subsystems under the mode-dependent average dwell time (MDADT) switching. A multiple convex Lyapunov function (MCLF) and a multiple piecewise convex Lyapunov function (MPCLF) are firstly proposed, which are formulated in a convex combination form of positive definite matrices with quasi-time-dependent coefficients. It is pointed out in the paper that the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF) can be regarded as special cases of the proposed MCLF and MPCLF, respectively. Then, the exponential stability conditions are derived by the new Lyapunov functions. Both slow switching and fast switching are exerted on stable modes and unstable modes, respectively. Finally, two numerical examples are given to demonstrate that larger stability regions and tighter MDADT bounds can be obtained by using our developed techniques compared with some recent results.
Year
DOI
Venue
2019
10.1016/j.amc.2019.01.065
Applied Mathematics and Computation
Keywords
Field
DocType
Switched systems,Multiple convex Lyapunov function,Multiple piecewise convex Lyapunov function,Exponential stability,Mode-dependent average dwell time
Dwell time,Lyapunov function,Matrix (mathematics),Convex combination,Mathematical analysis,Positive-definite matrix,Exponential stability,Discrete time and continuous time,Mathematics,Piecewise
Journal
Volume
ISSN
Citations 
353
0096-3003
1
PageRank 
References 
Authors
0.35
0
4
Name
Order
Citations
PageRank
Ruihua Wang1112.96
Ticao Jiao2445.50
Tao Zhang3234.46
Shu-Min Fei4115096.93