Delay-dependent stability and stabilizability of uncertain jump bilinear stochastic systems with mode-dependent time-delays

Abstract

This paper considers the problems of robust stability and robust stabilizability for a class of uncertain jump bilinear stochastic systems with mode-dependent time delays. By transforming the jump system under consideration into an equivalent descriptor jump system, a new stochastic Lyapunov functional is introduced for stability analysis and control design. Novel delay-dependent sufficient conditions in terms of linear matrix inequalities are derived for robust stability and robust stabilizability. Two numerical examples are given for the illustration of the proposed theoretical results.