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

• Grant number: 19/09363-5
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2019
• End date: January 31, 2023
• Field of knowledge: Engineering - Electrical Engineering
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Pedro Luis Dias Peres
• Grantee: Amanda Spagolla
• Host 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.

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SPAGOLLA, AMANDA; LEMAIRE, ALVARO A.; MORAIS, CECILIA F.; OLIVEIRA, RICARDO C. L. F.; PERES, PEDRO L. D.. Robust H-2 and H-8 control for positive continuous-time uncertain linear systems. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, v. 359, n. 10, p. 14-pg., 2022-07-01. (19/09363-5)

SPAGOLLA, AMANDA; MORAIS, CECILIA F.; OLIVEIRA, RICARDO C. L. F.; PERES, PEDRO L. D.. Stabilization and H-2 Static Output-Feedback Control of Discrete-Time Positive Linear Systems. IEEE Transactions on Automatic Control, v. 67, n. 3, p. 7-pg., 2022-03-01. (19/09363-5)

SPAGOLLA, AMANDA; MORAIS, CECILIA F.; OLIVEIRA, RICARDO C. L. F.; PERES, PEDRO L. D.; IEEE. H-infinity static output-feedback control for positive uncertain discrete-time linear systems. 2019 IEEE 58TH CONFERENCE ON DECISION AND CONTROL (CDC), v. N/A, p. 6-pg., 2019-01-01. (19/09363-5, 17/18785-5)

SPAGOLLA, AMANDA; MORAIS, CECILIA F.; OLIVEIRA, RICARDO C. L. F.; PERES, PEDRO L. D.. Reduced Order Positive Filter Design for Positive Uncertain Discrete-Time Linear Systems. IEEE CONTROL SYSTEMS LETTERS, v. 6, p. 1148-1153, 2022. (19/09363-5)

LEMAIRE, ALVARO A.; SPAGOLLA, AMANDA; MORAIS, CECILIA F.; OLIVEIRA, RICARDO C. L. F.; PERES, PEDRO L. D.. An LMI-based algorithm for static output-feedback stabilization of continuous-time positive polytopic linear systems. IFAC PAPERSONLINE, v. 53, n. 2, p. 6-pg., 2020-01-01. (17/18785-5, 19/09363-5)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SPAGOLLA, Amanda. Control of positive uncertain linear systems by means of linear matrix inequalities. 2023. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação Campinas, SP.