Research Papers

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
e-mail: ccku@mail.ntou.edu.tw

Guan-Wei Chen

Department of Marine Engineering,
National Taiwan Ocean University,
Keelung 202, Taiwan
e-mail: h60137@hotmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 27, 2016; final manuscript received March 3, 2017; published online June 13, 2017. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 139(10), 101004 (Jun 13, 2017) (11 pages) Paper No: DS-16-1215; 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 the 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 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 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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