LMI Conditions for Stability and Stabilization of Uncertain Discrete-time Switched Linear Systems

• Grant number: 18/05483-3
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: October 01, 2018
• End date: March 31, 2019
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Pedro Luis Dias Peres
• Grantee: Ariádne de Lourdes Justi Bertolin
• Supervisor: Sophie Tarbouriech
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Laboratoire d'Analyse et d'Architecture des Systèmes (LAAS), France
• Associated to the scholarship: 16/22020-1 - Robust Stability of Uncertain Time-varying Discrete-time Systems by means of Linear Matrix Inequalities, BP.MS

Abstract

The aim of the master project is to study the stability of uncertain time-varying discrete-time systems by means of Linear Matrix Inequalities (LMIs). The uncertain systems are represented by polytopic models, with time-invariant or time-varying parameters. In the time-varying case, the parameters can vary arbitrarily, can have bounded variations or can be described by a known dynamic linear equation. As strategy, the redundant description of the system and stability certificates provided by parameter-dependent Lyapunov functions are used, resulting on parameter-dependent stability conditions with extra parameter-dependent variables that can be solved through LMI relaxations. Numerical experiments involving comparison with other conditions from the literature will be performed, using computational tools available in Matlab to program the LMIs, together with parsers and solvers of public domain. The aim of this Research Internship Abroad~(BEPE) is to extend the original project to cope with uncertain discrete-time switched (possibly path constrained) linear systems as well, addressing the problems of robust stability, performance and state feedback stabilization.