Optimal Guaranteed Cost Control of Linear Systems with Mixed Interval Time-Varying Delayed State and Control

M. V. Thuan () and V. N. Phat ()
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M. V. Thuan: Thai Nguyen University
V. N. Phat: VAST

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 2, No 7, 394-412

Abstract: Abstract This paper deals with the problem of optimal guaranteed cost control for linear systems with interval time-varying delayed state and control. The time delay is assumed to be a continuous function belonging to a given interval, but not necessary to be differentiable. A linear–quadratic cost function is considered as a performance measure for the closed-loop system. By constructing a set of augmented Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a guaranteed cost controller design is presented and sufficient conditions for the existence of a guaranteed cost state-feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

Keywords: Guaranteed cost control; Stability; Stabilization; Interval delay; Lyapunov method; Linear matrix inequality (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9920-5

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