Non-Fragile H∞ Control for Piecewise Homogeneous Hidden Semi-Markov Lur’e Systems

In this brief the non-fragile asynchronous control problem is investigated for discrete-time non-homogeneous hidden semi-Markov Lur’e systems subjected to incapability obtained system mode and gain uncertainty, in which each subsystem is composed of mode-independent linear and nonlinear part. The non-homogeneous semi-Markov chain is established by a set of finite consecutive homogeneous semi-Markov chains with different intervals. To make the investigated problem more comprehensive, both the embedded Markov chain and sojourn-time probability density function in semi-Markov chain are considered to be piecewise-homogeneous. Particularly, they are regarded as simultaneously piecewise-homogeneous. Furthermore, with regard to the random occurrence gain uncertainty and mode uncertainty in the execution of actuators, this brief is devoted to designing a non-fragile asynchronous controller that can ensure the mean-square exponentially stability and $H_{\infty }$ performance of the resulting systems. In the final, an illustrative simulation is presented to demonstrate the feasibility of the derived results.