Asynchronous event-triggered guaranteed cost control of uncertain 2-D Bernoulli jump Roesser systems with actuator saturation and general transition probabilities

This paper investigates the problem of asynchronous event-triggered guaranteed cost control for uncertain two-dimensional Bernoulli jump systems with actuator saturation and general transition probabilities. First, a hidden Bernoulli model is adopted to characterize the mode mismatch phenomenon between the system mode and the controller mode in practical applications. Second, an event-triggered mechanism based on the hidden Bernoulli model is developed in the controller design to conserve communication resources. Third, a convex hull representation is utilized to address saturated inputs, and parameter uncertainties are integrated into the system model. Moreover, since precise transition probabilities of the Bernoulli process and the observation process are difficult to determine, general transition probabilities in the two processes are considered simultaneously. By using quadratic Lyapunov function techniques combined with linear matrix inequality approaches, sufficient conditions are established to ensure that the resulting closed-loop system is asymptotically mean square stable and satisfies the guaranteed cost performance under three distinct boundary conditions with or without general transition probabilities. Finally, a convex optimization algorithm is proposed for the design of the optimal asynchronous event-triggered guaranteed cost control law, and its effectiveness is demonstrated through a numerical example.