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Technical Briefs

Delay-Dependent Stabilization of Discrete-Time Systems With Time-Varying Delay via Switching Technique

[+] Author and Article Information
Hui Zhang

Department of Mechanical Engineering,  University of Victoria, P.O. Box 3055, STN CSC, BC, V8W 3P6, Victoria Canadahuizhang@uvic.ca

Yang Shi1

Department of Mechanical Engineering,  University of Victoria, P.O. Box 3055, STN CSC, BC, V8W 3P6, Victoria Canadayshi@uvic.ca

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(4), 044503 (May 07, 2012) (5 pages) doi:10.1115/1.4006218 History: Received December 21, 2010; Revised December 31, 2011; Published May 04, 2012; Online May 07, 2012

In this paper, we investigate the stabilization problem of time-delay discrete-time systems with occurrence probabilities for time delays. Using an augmenting technique, we convert random time-delay discrete-time systems to delay-free systems with stochastic variables. We propose to design a sequence of delay-dependent controllers. The implemented controller is chosen according to the measured time delay at each sampling instant. When the delay is randomly time-varying, the implemented controller is switched in a designed controller set. An example is provided to illustrate the effectiveness of the stability condition and another example is offered to show the applicability of the proposed design algorithm.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Maximum absolute value of eigenvalues of A¯d(k)

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Figure 2

Time-varying delay with equal probability

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Figure 3

Trajectories of the states in a random simulation run

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