On stability and stabilisation of continuous-time singular Markovian switching systems

The class of continuous-time singular linear systems with Markovian switching is presented. Under full and partial knowledge of the jump rates of the continuous-time Markov process sufficient conditions in the linear matrix inequality setting for the system to be piecewise regular, impulse-free and stochastically stable are developed. A state feedback controller that makes the closed-loop system piecewise regular, impulse-free and stochastically stable is also designed. Full and partial knowledge of the jump rates are considered. Numerical examples are proposed to show the validness of the developed results.