Delay-dependent stability analysis for singular Markovian jump systems with incomplete transition probabilities

This paper investigates the problem of stochastic stability analysis for a class of discrete-time singular Markovian jump systems with time-varying delays and incomplete (i.e., unknown and uncertain) transition probabilities. To derive an improved delay-range-dependent stability criterion under the incomplete transition descriptions, a relaxation scheme is proposed with consideration of the free-weighting matrix method compatible with the delay partitioning technique, and its purpose is accomplished (1) by making full use of the available boundary information on incomplete transition probabilities, and (2) by employing novel slack variables that allow some useful equality constraints to be exploited.