Robust stability, stabilization and L2-gain analysis of uncertain switched linear systems

Abstract

This paper considers the robust stability, stabilization and L 2 -gain analysis of switched linear systems in the simultaneous presence of uncertainty and exogenous disturbance inside subsystems. State feedback and output feedback controllers, together with minimal dwell time (MDT) based switching signal, are designed to achieve the objective that, on the one hand, the closed-loop system without exogenous disturbance input is robustly asymptotically stable with respect to system uncertainty, and on the other hand, the closed-loop system with the presence of exogenous disturbance input has a pre-given L 2 -gain with respect to the input-output relationship with the input be the exogenous disturbance and the output be the system's given quantities. The control synthesis is performed by means of linear matrix inequalities (LMIs), and thus it is numerically tractable.