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

Rongwei Guo

doi:10.1155/2014/214756

Abstract

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.

Highlights

Switched systems arise in various fields of real life world, such as manufacturing, communication networks, autopilot design, automotive engine control, computer synchronization, traffic control, and chemical processes
Motivated by the above reasons, we extend our previous results in [17, 18] to investigate the stability of SN system in both cases: one is where all subsystems are GAS, the other is where both GAS and unstable subsystems coexist
As the authors in [16] point out that the property in the ADT switching, that the average time interval between any two consecutive switching is at least τa∗, which is independent of the system modes, is probably still not anticipated

Summary

Introduction

Switched systems arise in various fields of real life world, such as manufacturing, communication networks, autopilot design, automotive engine control, computer synchronization, traffic control, and chemical processes. There are several important problems to be investigated, such as stability analysis and control design. Abstract and Applied Analysis deal with the SL system with stable and unstable subsystems, the ADT method used in such paper has two disadvantages: one is this ADT method is only used for the SL system, the other is the lower bound of ADT τa∗ obtained by the results in [12] has much conservative property. To obtain an improved ADT method for the SN systems with stable and unstable subsystem is very important, and to investigate this problem is of value both in theory and in practice.

Problem Formulation

Main Results

Illustrative Examples

Conclusions