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

摘要

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. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.