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, cilt.38, sa.1, ss.125-142, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1093/imamci/dnaa003
  • Dergi Adı: IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Compendex, INSPEC, zbMATH
  • Sayfa Sayıları: ss.125-142
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.