Control of Linear Systems Case

This chapter investigates the \(H_{\infty }\) control problem of linear Markov jump singularly perturbed systems (MJSPSs), in which the complete probability information case, partial probability information case and general probability information case are fully considered. Both the mode-dependent \(H_{\infty }\) controller and mode-independent one design methods are presented for the above three probability information cases. Finally, the effectiveness and applicability of the proposed control law is illustrated by a numerical example.