Stabilisation of mode-dependent singular Markovian jump systems with generally uncertain transition rates

This paper is devoted to investigating the stability and stabilisation problems for continuous-time mode-dependent singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs). First, we establish a sufficient condition in terms of a set of coupled linear matrix inequalities (LMIs) to ensure the systems to be regular, impulse-free and stochastically stable. Then, we design a mode-dependent state-feedback controller to guarantee the closed-loop systems stochastically admissible by applying the LMI technique. Finally, a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method.