A PRIVATE SOLUTION OF THE BROKETT STABILIZATION PROBLEM

Authors

  • Sh.A. Aipanov
  • S.A. Medetbaeva Almaty Technological University, Kazakhstan

Keywords:

control of a kind, kind, matrix, auxiliary problem, system, differential equation

Abstract

In the present paper, sufficient conditions are obtained under which the system will be not only asymptotically stable in the sense of Lyapunov, but also exponentially stable in the whole (i.e., under any initial conditions). In addition, a constructive method is proposed for choosing a matrix that solves Brockett's problem.

References

Brockett R. A stabilization problem // In: Open Problems in Mathematical Systems and Con-trol Theory. – London: Springer, 1999. – P. 75-78.

Moreau L., Aeyels D. Stabilization by means of periodic output feedback // 38th IEEE Confer-ence on Decision and Control: Conference Proceedings. – Arisona, 1999. – P. 108-109.

Leonov G.A. The Brockett stabilization problem // Automation and Remote Control, vol. 62, No. 5, 2001. – P. 847-849.

Leonov G.A. The Brockett problem for linear discrete control systems // Automation and Re-mote Control, vol. 63, No. 5, 2002. – P. 777-781.

Ройтенберг Я.Н. Автоматическое управление. М.: Наука, 1992. – 576 с.

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Published

2022-07-04

Issue

Section

ANALYSIS AND SYNTHESIS OF CONTROL SYSTEMS