Observer-based controller design for nonlinear semi-Markov switched system with external disturbance

Abstract

This paper focuses on the observer-based controller design problem for uncertain continuous-time nonlinear switched system with semi-Markov random switching signal. The mode transition rates (TRs) of switched system rely on the random sojourn-time instead of the constant. By considering the distribution of external disturbances, the nonlinear switched system is transformed into an augmented switched system, where the external disturbance is decoupled as a part of the state of the augmented system. Then, a stochastically switching observer is proposed to simultaneously estimate the state and external disturbance, and a sufficient condition on the stochastic stability of state estimation error dynamics is presented by constructing a semi-Markov Lyapunov function and using linear matrix inequality (LMI) technique. Furthermore, a stochastically switching controller is synthesized to guarantee the stochastic stability of the closed-loop switched system with external disturbance. Finally, an illustrative example is given to validate the effectiveness of the proposed approach.