Discrete procedure of optimal stabilization for periodic linear systems of differential equations

R. I. Shevchenko^a, Yu. F. Dolgii<sup>b

a</sup> Experimental Machine Design Bureau «Novator»
^b N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences

Abstract: We propose procedure to solve the optimal stabilization problem for linear periodic systems of differential equations. Stabilizing controls, formed as a feedback, are defined by the system states at the fixed instants of time. Equivalent discrete-time linear periodic problem of optimal stabilization is considered. We propose a special procedure for the solution of discrete periodic Riccati equation. We investigate the relation between continuous-time and discrete-time periodic optimal stabilization problems. The proposed method is used for stabilization of mechanical systems.

Keywords: linear periodic system, discrete-time periodic optimal stabilization problem, discrete periodic Riccati equation.

UDC: 517.927

Received: 16.04.2018

DOI: 10.20310/1810-0198-2018-23-124-891-906

Bibliographic databases:

•