Dynamic event‐based dissipative asynchronous control for singular Markov jump LPV systems with general transition rates

Abstract

Abstract In this article, the dissipative asynchronous control is investigated for a series of continuous‐time singular Markov jump linear parameter‐varying (SMJLPV) systems under a dynamic event‐triggered scheme, in which the system parameters depend on the measured parameters in real time. The dynamic event‐triggered scheme (DES) is used to bring down the channel congestion caused by the limited bandwidth and raise the utilisation ratio of network resources. Then, the Markov chains of SMJLPV systems with partially known transition rates are discussed, which can further reduce the conservatism to some extent. Specifically, since the controller cannot accurately receive the modes information of the system in real time, the hidden Markov model is established to depict the asynchronous phenomenon. Next, in the light of the parameter‐dependence Lyapunov functional, the criteria of stochastically admissible for the considered SMJLPV systems with the given dissipative performance is obtained. In such context, parameter‐dependent linear matrix inequalities are obtained and a cooperative design method of asynchronous controller and the weighting matrix of the DES is proposed. Finally, numerical examples under two different event‐triggered schemes are given to verify the effectiveness of the proposed method.