Control of uncertain positive linear systems by means of linear matrix inequalities

• Grant number: 19/09363-5
• Support type: Scholarships in Brazil - Doctorate
• Effective date (Start): August 01, 2019
• Effective date (End): January 31, 2022
• Field of knowledge: Engineering - Electrical Engineering
• Cooperation agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Pedro Luis Dias Peres
• Grantee: Amanda Spagolla
• Home Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The aim of this project is to study linear positive systems, that is, linear systems where the state and output are both nonnegative for any nonnegative initial state and nonnegative input, in both continuous and discrete-time cases. The goal is to propose conditions for stability analysis and synthesis of control laws for positive linear systems based on Linear Matrix Inequalities (LMIs), taking into account parametric uncertainties in the model and performance criteria such as the H, H2 and L1 norms. The methodology relies on Lyapunov's theory, using polynomially parameter-dependent functions to build certificates for closed-loop stability and performance, together with strategies that introduce slack variables and provide conditions in terms of robust (or parameter-dependent) LMIs, that can be numerically solved through LMI relaxations. Extensions to consider saturation in the control signal, dynamic controllers, filter design, time-varying parameters and gain-scheduling will be investigated. Comparative numerical studies with other methods from the literature will be conducted.