Observer-based controller design of Markovian jump bilinear descriptor systems

In this paper, we consider the problem of designing an observer-based output feedback controller for the class of Markovian jump bilinear descriptor systems (MJBDS). First, we investigate the existence and the uniqueness of the solution, then we derive sufficient conditions that guarantee the regularity, absence of impulses and stochastic stability in asymptotic mean-square sense of the closed-loop system. Based on linear matrix inequality approach (LMI), all results are expressed in terms of a set of strict LMIs, which are more reliable in numerical computation. A numerical example is provided to demonstrate the applicability of the proposed approach