Domain of attraction of saturated switched systems under dwell-time switching

TL;DR

This paper develops a convex LMI-based method to estimate the domain of attraction for saturated switched systems under dwell-time constraints, improving stability analysis accuracy.

Contribution

It introduces a novel LMI-based approach using multiple Lyapunov functions and polytopic saturation representation for stability and domain of attraction estimation.

Findings

Less conservative stability conditions than existing methods

Efficient LMI formulation for domain of attraction estimation

Numerical examples demonstrate improved stability margins

Abstract

This paper considers discrete-time switched systems under dwell-time switching and in the presence of saturation nonlinearity. Based on Multiple Lyapunov Functions and using polytopic representation of nested saturation functions, a sufficient condition for asymptotic stability of such systems is derived. It is shown that this condition is equivalent to linear matrix inequalities (LMIs) and as a result, the estimation of domain of attraction is formulated into a convex optimization problem with LMI constraints. Through numerical examples, it is shown that the proposed approach is less conservative than the others in terms of both minimal dwell-time needed for stability and the size of the obtained domain of attraction.