Stabilization for switched linear systems: Hybrid observer‐based method

Abstract

This paper investigates interval observer-based controller design for switched linear systems involving additional disturbance and measurement noise, whose modes need not to be cooperative. First, by giving the upper bound and the lower bound of the disturbance and the measurement noise, we construct hybrid interval observer for the considered switched linear system by means of a switched coordinate transformation, which can transform the observer error systems into cooperative ones. The interval observer can supply certain state information at any instant. Compared with the interval observer design for switched systems with arbitrary switching sequences or dwell time switching based on common Lyapunov function, the difficulty consists in characterizing the jump of the multiple Lyapunov functions. Then, by using the multiple Lyapunov functions method and average dwell time scheme, some sufficient conditions are derived and applied to build the interval observer-based state feedback controller. Finally, we provide an example to illustrate the validity of the derived results.