Observer-Based Asynchronous Guaranteed Cost Control of 2-D Markov Jump Roesser Systems With Nonideal Transition Probabilities

This paper mainly investigates the asynchronous observer-based guaranteed cost control problem for two-dimensional Markov jump Roesser systems with nonideal transition probabilities. First, a hidden Markov model is developed to describe the asynchronous phenomenon caused by the mode mismatch between the controlled system and the controller. Second, an asynchronous observer-based feedback control law based on the hidden Markov model is designed against the inaccessibility of the system states. Third, since accurate transition probabilities of the Markov chain and the hidden Markov process are difficult to obtain, nonideal transition probabilities are simultaneously considered in both mode transition and mode observation processes. By using the quadratic Lyapunov function techniques and linear matrix inequality methods, some sufficient criteria are developed such that the resultant closed-loop system is asymptotically stable with/without nonideal transition probabilities and satisfies a guaranteed cost performance under three different boundary conditions. Finally, an asynchronous observer-based optimal guaranteed cost controller design algorithm is proposed and two numerical examples are considered to demonstrate its effectiveness.