Robust stabilizability and stabilization of three-time-scale linear time-invariant singularly perturbed systems with delay
https://doi.org/10.29235/1561-2430-2023-59-2-110-120
Abstract
The objective of this study is to obtain the stabilizability conditions and a stabilizing composite state feedback control for the exponential stabilization of three-time-scale singularly perturbed linear time-invariant systems with multiple commensurate delays in the slow state variables and with two small parameters of perturbation (TSPLTISD). The stabilizability conditions and the stabilizing feedback do not depend on the small parameters and are valid for all of their sufficiently small values. The approach used in this work is the nondegenerate decoupling transformation that splits the TSPLTISD into three regularly dependent on the small parameters subsystems, which are lower in dimensions than the TSPLTISD. Further, the decoupled subsystems are approximated by three subsystems that do not depend on the small parameters. It is proven that the stabilizability of the approximating subsystems guarantees the robust (with respect to small parameters) stabilizability of the original TSPLTISD. Finally, we obtain a representation of a parameter free composite feedback control for the TSPLTISD, stabilizing it for all sufficiently small values of the parameters. A numerical example is given.
About the Authors
Ch. A. Naligama
Yanka Kupala State University of Grodno; Cenex Engineering
Belarus
Belarus
Chamila A. Naligama – Postgraduate Student, Department of Mathematics and Informatics; Consulting Engineer
22, Ozheshko Str., 230023, Grodno; 550/01/10, Mihindumawatha, Malwatta, Nittambuwa, Sri Lanka, 11880
O. B. Tsekhan
Yanka Kupala State University of Grodno
Belarus
Belarus
Olga B. Tsekhan – Ph. D. (Physics and Mathematics),
Associate Professor, Associate Professor of the Department
of Mathematical and Information Support of Economic
Systems
22, Ozheshko Str., 230023, Grodno
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