Controller Design Based on Interval-observer for Switched Systems With Observer-state-dependent Switching

In this paper, we study the problem of interval-observer based controller design for switched linear systems with disturbance and measurement noise. First, we propose the definition of finite-time interval-observers for switched systems and construct finite-time interval-observers for switched linear systems with observer-state-dependent switching strategy by giving the ranges of the external disturbance and the measurement noise. Then, by using multiple Lyapunov functions method, some sufficient conditions are provided to guarantee the existence of the finite-time interval-observers under maximum constraints, and at the same time, based on the proposed sufficient conditions, the observer gains are given and the corresponding sliding motion issue is also solved. After that, we design an interval-observer-based feedback controller for the switched systems. Different from the traditional observer-based controller with state-dependent switching signal designed in most literatures, the controller designed in the paper is based on interval-observer with observer-state-dependent switching signal. Compared with the traditional observers, the interval-observers are robust to large uncertainties and can provide the ranges of the system states in any time. Finally, the feasibility of the proposed method is verified by two numerical examples.