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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.

Normalised stabilisation for singular semi-Markov jump systems with discontinuous jump states