Robust guaranteed cost control for time-delayed stochastic systems with Markovian switching

The problem of the robust guaranteed cost control for time-delay stochastic systems with Markov switching parameters is discussed. First, the definition of such systems' robust guaranteed cost control is given, the Lyapunov function is constructed, and the Ito differential formula is applied to compute the differential of such functional along the system. Then applying the character of LMI and the generalized Ito formula, the sufficient condition of the existence of such control law is given, and the robust guaranteed cost value is also given. And the design of robust guaranteed cost controllers is concluded as solving a cluster of LMIs. A numerical example is presented to show that the result is efficient.