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Automation and Remote Control

, Volume 76, Issue 5, pp 801–808 | Cite as

About the necessity of Popov criterion for a special Lyapunov function existence for the systems with multiple nonlinearities

  • M. M. Lipkovich
  • A. L. Fradkov
Topical Issue

Abstract

Necessary and sufficient conditions for existence of Lyapunov function from the class “quadratic form plus integral of nonlinearity” (Lyapunov-Lurie function) for systems with several nonlinearities are considered. It is assumed that the nonlinearity graphs belong to the infinite sectors, i.e., belong to the union of the first and third quadrants in the plane. It is proven that Popov criterion is necessary and sufficient for existence of Lyapunov-Lurie function if the relative degree of the linear part is greater than one. The proof is based on the result concerning losslessness of the S-procedure for several respective quadratic constraints.

Keywords

Remote Control Lyapunov Function Absolute Stability Domain Condition Nonlinear Control System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Saint Petersburg State UniversitySt. PetersburgRussia
  2. 2.Institute of Problems of Mechanical EngineeringSt. PetersburgRussia
  3. 3.ITMO UniversitySt. PetersburgRussia

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