Constructing alternative certificates for polynomial positivity with Bernestein's and Handelman's basis

• Grant number: 23/14906-3
• Support Opportunities: Scholarships abroad - Research Internship - Scientific Initiation
• Start date: February 01, 2024
• End date: May 31, 2024
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Pedro Luis Dias Peres
• Grantee: Gabryelle Jesus de Souza
• Supervisor: Giorgio Valmorbida
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: École Centralesupélec, France
• Associated to the scholarship: 23/03051-7 - Robust stability analysis of uncertain linear systems through the Liénard-Chipart criterion, BP.IC

Abstract

The original Scientific Initiation project aims to study the problem of robust stability analysis for linear systems with uncertain parameters by means of 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.The aim of this Research Internship Abroad (BEPE-IC) is to investigate strategies to certificate polynomial positivity in terms of Bernstein's basis and Handelman's basis, as well as to add domain partitioning techniques to the algorithms.