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Optimal stabilization for differential systems with delays – Malkin’s approach. (English) Zbl 1414.93160
Summary: The paper considers a process controlled by a system of delayed differential equations. Under certain assumptions, a control function is determined such that the zero solution of the system is asymptotically stable and, for an arbitrary solution, the integral quality criterion with infinite upper limit exists and attains its minimum value in a given sense. To solve this problem, Malkin’s approach to ordinary differential systems is extended to delayed functional differential equations, and Lyapunov’s second method is applied. The results are illustrated by examples, and applied to some classes of delayed linear differential equations.

MSC:
93D20 Asymptotic stability in control theory
93C23 Control/observation systems governed by functional-differential equations
49K40 Sensitivity, stability, well-posedness
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