An Extension of the Invariance Principle for Switched Affine System

Abstract

In this paper, an approach to investigate switched affine system via matrix inequalities is presented. Particularly, an extension of LaSalle’s invariance principle for this class of systems under arbitrary dwell-time switching signal is presented. The proposed results employ a common auxiliary scalar function and also multiple auxiliary scalar functions to study the asymptotic behavior of switched solutions and estimate their attractors for any dwell-time switching signal. A specific feature of these results is that the derivative of the auxiliary scalar functions can assume positive values in some bounded sets. Moreover, a problem of constrained optimization is formulated to numerically determine the auxiliary scalar functions and minimize the volume of the estimated attractor. Numerical examples show the potential of the theoretical results in providing information on the asymptotic behavior of solutions of the switched affine systems under arbitrary dwell-time switching signals.

Keywords

• Switched affine system
• invariance principle
• dwell-time
• attractor set.