H2 and H∞ Control with sector bound optimization for Continuous Time Markov Jump Lur’e Systems

Abstract

This paper addresses the $H_2$ and $H_{\infty }$ control of Markov Jump Systems subject to a class of nonlinearities that include them on the Lur’e system framework, with sector slope optimization. The proposed controllers are robust to nonlinearities belonging to a sector. We propose mode-dependent controllers; in other words, the Markov mode $\theta \left(t\right)$ is available to controllers. The design of such controllers considers the optimization of the $H_2$ and $H_{\infty }$ costs as well as the sector slope, which determines the class of accepted nonlinearities. The results are illustrated through two practical examples: coupled electrical machines and the semi-active suspension of a quarter car.