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Optimal guaranteed cost control of linear systems with mixed interval time-varying delayed state and control. (English) Zbl 1237.49047
Summary: 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 illustrate the effectiveness of the obtained result.

49N10Linear-quadratic optimal control problems
49K40Sensitivity, stability, well-posedness of optimal solutions
34H05ODE in connection with control problems
49M30Other numerical methods in calculus of variations
Full Text: DOI
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