Novel Criteria of Stochastic Stability for Discrete-Time Markovian Jump Singular Systems via Supermartingale Approach

This article deals with the problem of stochastic stability for a class of discrete-time Markovian jump singular systems. A time-dependent coordinate transformation is provided, under which an equivalent form of the original Markovian jump singular systems can be obtained. This equivalent form not only shows the inherent state jump behavior at the switching instants, but also plays an important role in the stochastic stability analysis. Constructing a supermartingale over some $\sigma$ -algebra together with the property of conditional expectation, a necessary and sufficient condition is established to ensure that the equilibrium point of the underlying system is exponentially stable in mean square. Two numerical examples are given to illustrate the effectiveness of the developed results.