Delay-Dependent Robust Control for Discrete-Time Uncertain Stochastic Systems with Time-Varying Delays

[+] Author and Article Information
Cheung-Chieh Ku

Department of Marine Engineering National Taiwan Ocean University Keelung 202, Taiwan, China

Guan-Wei Chen

Department of Marine Engineering National Taiwan Ocean University Keelung 202, Taiwan, China

1Corresponding author.

ASME doi:10.1115/1.4036365 History: Received April 27, 2016; Revised March 03, 2017


This paper investigates a delay-dependent robust control problem of discrete-time uncertain stochastic systems with delays. The uncertainty considered in this paper is time-varying but norm-bounded, and the delays are considered as interval time-varying case for both state and input. According to considerations of uncertainty, stochastic behavior and time-delays, the problem considered in this paper is more general than the existing works for uncertain stochastic systems. Via the proposed Lyapunov-Krasovskii function, some sufficient conditions are derived into the extended Linear Matrix Inequality (LMI) form. Moreover, Jensen Inequality and free matrix equation are employed to reduce conservatism of those conditions. Through using the proposed design method, a Gain-Scheduled (GS) controller is designed to guarantee asymptotical stability of uncertain stochastic systems in the sense of mean square. Finally, two numerical examples are provided to demonstrate applicability and effectiveness of the proposed design method.

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