Paper Info
Title
On the (h0,h)-stabilization of switched nonlinear systems via state-dependent switching rule
Abstract
This paper considers switching stabilization of some general nonlinear systems. Assuming certain properties of a convex linear combination of the nonlinear vector fields, two ways of generating stabilizing switching signals are proposed, i.e., the minimal rule and the generalized rule, both based on a partition of the time-state space. The main theorems show that the resulting switched system is globally uniformly asymptotically stable and globally uniformly exponentially stable, respectively. It is shown that the stabilizing switching signals do not exhibit chattering, i.e., two consecutive switching times are separated by a positive amount of time. In addition, under the generalized rule, the switching signal does not exhibit Zeno behavior (accumulation of switching times in a finite time). Stability analysis is performed in terms of two measures so that the results can unify many different stability criteria, such as Lyapunov stability, partial stability, orbital stability, and stability of an invariant set. Applications of the main results are shown by several examples, and numerical simulations are performed to both illustrate and verify the stability analysis.
Year
DOI
Venue
2010
10.1016/j.amc.2010.07.007
Applied Mathematics and Computation
Keywords
Field
DocType
Switched system,Switching stabilization,Nonlinear system,Switching control,Stability analysis,Two measures,Lyapunov method
Linear combination,Mathematical optimization,Nonlinear system,Vector field,Control theory,Lyapunov stability,Exponential stability,Invariant (mathematics),Partition (number theory),Mathematics,Stability theory
Journal
Volume
Issue
ISSN
217
5
0096-3003
Citations 
PageRank 
References 
8
0.66
6
Authors
3
Name
Order
Citations
PageRank
Jun Liu121520.63
Xinzhi Liu21318106.23
Wei-Chau Xie327612.07