Robust stability analysis of uncertain linear systems through the Liénard-Chipart criterion

• Grant number: 23/03051-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2023
• End date: September 30, 2024
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Pedro Luis Dias Peres
• Grantee: Gabryelle Jesus de Souza
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 23/14906-3 - Constructing alternative certificates for polynomial positivity with Bernestein's and Handelman's basis, BE.EP.IC

Abstract

The aim of this plan is to study the problem of robust stability analysis for linear systems with uncertain parameters. In the literature, most approaches are based on Lyapunov's stability theory, generally resulting in tests formulated as Linear Matrix Inequalities (LMIs). LMIs are convex optimization problems that can be solved by algorithms with proven efficiency. Particularly for the class of continuous-time linear systems with uncertain parameters, this plan investigates an alternative stability condition based on Hurwitz determinants, known as the Liénard-Chipart criterion, which expresses the problem in terms of the analysis of a scalar polynomial. To ensure that the stability test is conclusive, a procedure of domain partitioning is applied. For simplicity, only one uncertain parameter is considered in a first phase, with the posterior extension to two or three parameters. Exhaustive tests are carried out to evaluate the compromise between precision and computational effort for systems with different numbers of states, and the proposed method is also compared with some techniques based on LMIs. Computational tools available in Matlab for symbolic manipulation of polynomials, parsers and LMI solvers of public domain are used in the development of the research.