Guaranteed cost control for discrete-time Markovian jump linear system with time delay

The scaled small gain theorem is used to investigate the problem of guaranteed cost control for discrete-time Markovian jump systems with mode-dependent and time-varying delay in this article. For obtaining the results in this article, first a stochastic scaled small gain condition for discrete-time Markovian jump systems is introduced. Then, the original system is transformed into an input–output form. The robust stability criterion of the original system is proposed through the Lyapunov–Krasovskii functional approach combined with the utilisation of the stochastic small gain condition. The merit of the proposed criterion lies in its reduced conservatism, which is made possible by a precise approximation of the mode-dependent and time-varying delay. Furthermore, the guaranteed cost controller existence criterion is proposed by the robust stability criterion, which guarantees the robust stochastic stability of the closed-loop system and the existence of the upper bound for the cost function. Finally, two illustrative examples are provided to demonstrate the advantage and the effectiveness of the obtained results.