Robust stabilization of non-linear non-autonomous control systems with periodic linear approximation


Slyn'ko V., Tunç C., Bivziuk V. O.

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, vol.38, no.1, pp.125-142, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1093/imamci/dnaa003
  • Journal Name: IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Compendex, INSPEC, zbMATH
  • Page Numbers: pp.125-142

Abstract

The paper deals with the problem of stabilizing the equilibrium states of a family of non-linear non-autonomous systems. It is assumed that the nominal system is a linear controlled system with periodic coefficients. For the nominal controlled system, a new method for constructing a Lyapunov function in the quadratic form with a variable matrix is proposed. This matrix is defined as an approximate solution of the Lyapunov matrix differential equation in the form of a piecewise exponential function based on partial sums of a W. Magnus series. A stabilizing control in the form of a linear feedback with a piecewise constant periodic matrix is constructed. This control simultaneously stabilizes the considered family of systems. The estimates of the domain of attraction of an asymptotically stable equilibrium state of a closed-loop system that are common for all systems are obtained. A numerical example is given.