Robust state estimation for switched systems with unstable subsystems

In this paper, the robust state estimation problem is discussed for a class of switched continuous time systems with uncertainty. We do not require that all the subsystems of the switched system are stable. First, the definition of interval observers is extended to switched systems. Then, by giving the upper bound and the lower bound of the uncertainty and employing the multiple linear copositive Lyapunov function method and mode-dependent average dwell time scheme, some sufficient conditions are derived and applied to build the interval observer, which supply certain information at any instant: an upper bound and a lower bound are provided for each component of the states. Finally, a numerical example is proposed to illustrate the effectiveness of the main result.