Abstract
This paper addresses the almost surely exponential (ASE) stabilisation problem of continuous-time singular semi-Markov jump systems (s-MJSs), where the state at jump instants is discontinuous. Because of such a discontinuity existing, the consistency of initial condition at jump instants is impossible to be ensured but is an essential issue of singular systems. A proportional-derivative (PD) state feedback controller is proposed to deal with it such that the closed-loop singular s-MJSs is normal and ASE-stable. New sufficient conditions for the existence of such a controller are derived as linear matrix inequalities, which includes some existing considered systems as special situations. Two numerical examples are used to show the effectiveness and superiority of the methods.
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