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.

Keywords:

• Jump bilinear stochastic systems
• Delay-dependent stability
• Norm-bounded uncertainty
• Linear matrix inequality (LMI)
• Time-delay systems

Acknowledgement

This study was supported by the National Natural Science Foundation of China under Grant 60274004, 10461001.