Generalized Energy Functions for a Class of Third-Order Nonlinear Dynamical Systems

Author(s)

Costa Alberto, Luis Fernando ^[1] ; Siqueira, Daniel S. ^[1] ; Bretas, Newton Geraldo ^[1] ; Chiang, Hsiao-Dong ^[2]

Affiliation

^[1] Univ Sao Paulo, Sao Carlos Sch Engn, Elect & Comp Engn Dept, BR-05508220 Sao Carlos - Brazil

^[2] Cornell Univ, Sch Elect & Comp Engn, Ithaca, NY 14850 - USA

• Document type: Journal article
• Source: IEEE Transactions on Automatic Control; v. 66, n. 7, p. 3111-3122, JUL 2021.
• Web of Science Citations: 0

Abstract

Nonlinear dynamical systems exhibiting complex structure in their limit sets, such as chaotic and closed orbits, do not admit energy functions. The theory of generalized energy functions, which may assume positive derivative in some bounded sets, appears as an alternative to study the asymptotic behavior of solutions of these systems. In this article, a generalized energy function and a complete characterization of the stability boundary and stability region are developed for a class of third-order dynamical systems. This class of systems appears in electrical power system models and has a class of quasi-gradient systems and second-order systems as particular cases. These systems may admit complex structure in their limit sets and do not admit an energy function that is general for the class. Numerical examples illustrate how generalized energy functions provide estimates of stability regions. (AU)

• FAPESP's process: 11/23345-8 - General Energy Function of Control Applied to TCSC Regulators in Power Systems.
• Grantee: Daniel Souto Siqueira
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants