Finite-time robust observers for switched linear systems with state-dependent switching

The finite-time robust state observer design problem of switched linear systems in which both the external disturbance and the measurement noise are involved is studied here. Different from the existing literatures related to robust observers of switched systems, which consider arbitrary switching signals or dwell time switching signals, in this paper we consider state-dependent switching signals. We first propose the definition of finite-time interval observers for switched systems. Then, by giving the ranges of the external disturbance and the measurement noise, we construct finite-time interval observers for switched linear systems with state-dependent switching strategy. Next, by multiple Lyapunov functions method, some sufficient conditions characterizing the finite-time stability (FTS) of positive error systems under maximum constraints are derived and applied to solve the observer gains and the corresponding sliding motion issue is also discussed. Finally, an example on the state observers of switched systems is given for illustration.