Event-Triggered Control for Roesser Model-Based 2D Markov Jump Systems Under Stochastic Communication Protocol

This paper is concerned with the event-triggered control problem for Roesser model-based two-dimensional (2D) Markov jump systems with multiple communication channels. In order to optimize the utilization of communication resources, an event-triggered rule (ETR) is proposed based on the structural characteristics of the 2D Markov jump plant. In addition, a stochastic communication protocol (SCP) is utilized to schedule transmissions from the controller to the actuators. Under the ETR and the SCP, an asynchronous state-feedback control scheme is formulated, allowing for mode mismatches between the controller and the 2D plant. A sufficient condition on both stochastic stability and a predefined \({\mathcal {H}}_{\infty }\) ${\mathcal{H}}_{\infty }$ disturbance-attenuation performance of the closed-loop 2D system is established. Building upon this condition and linear matrix inequalities, a computationally efficient method is developed for designing the required state-feedback controller gains. Finally, the feasibility and effectiveness of the proposed event-triggered control approach are demonstrated by the application of a simulation example involving the Darboux equation.