Simultaneous Fault Detection and Control Design for Switched Linear Systems: A Linear Matrix Inequality Approach

Abstract

In this paper, the problem of simultaneous fault detection and control (SFDC) for linear switched systems in discrete- and continuous-time cases under a mixed H− /H∞ framework is considered. In essence, a single unit called detector/controller is designed, where the detector is an observer and the controller is an observer-based controller. The conventional mixed H− /H∞ problem is a conservative approach due to the selection of equal Lyapunov matrices. Extended linear matrix inequalities (LMIs) characterizations are used to reduce the conservativeness by the introduction of additional matrix variables, so as to eliminate the coupling of Lyapunov matrices with the system matrices. Indeed, the idea presented in this paper is based on the average dwell time (ADT) and conservatism reduction approaches, which lead to some sufficient conditions for solving the problem in terms of LMI feasibility conditions. Two examples are provided to demonstrate the effectiveness of the proposed method.