Dissipative Tracking Control of Nonlinear Markov Jump Systems With Incomplete Transition Probabilities: A Multiple-Event-Triggered Approach

Abstract

This paper deals with the problem of multiple-event-triggered dissipative tracking control for nonlinear Markov jump systems (MJSs) with incomplete transition probabilities. An interval type-2 (IT2) fuzzy model with partially known transition probability matrix (TPM) is used to capture the underlying nonlinearities, and a hidden Markov model (HMM) with an incomplete conditional probability matrix (CPM) is employed to describe the possible asynchronous phenomenon between the plant and the tracking controller. A multiple-event-triggered methodology involving two adaptive event-triggered schemes (AETS) for the actuator channel and the sensor channel is proposed. By using the Lyapunov and dissipativity theory, sufficient conditions for the desired tracking controller are established in terms of linear matrix inequalities (LMIs). Last, two examples, involving one numerical and one practical model named the Hénon system, are utilized to show the effectiveness of the proposed tracking control algorithm.