Optimal stabilization for differential systems with delays - Malkin’s approach

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článek v časopise ve Web of Science, Jimp
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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.

Klíčová slova
Differential equation
Delay
control
quality criterion
asymptotic stability