H∞ control of time-delay state feedback Markovian jump linear systems with uncertain transition rates

This paper deals with the H∞ time-delay control problem for a class of uncertain Markovian jump linear systems (MJLSs). Since it's difficult to obtain the transition rates of real control systems, we consider the systems with uncertain transition rates. Combining H∞ control theory, we propose a sufficient robust stochastic stability criterion of the system. Then, the H∞ time-delay state-feedback controller that makes the underlying system stabilizable with γ-disturbance attenuation is designed. By constructing a Lyapunov functional, the time-delay independent LMI-formatted globally stability criterion is proposed based on robust control theory. Then, numerical example is provided to demonstrate the effectiveness of the derived results.