Abstract
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.