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

Author(s)

Amanda Spagolla

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2023-06-01

Examining board members

Pedro Luis Dias Peres; Matheus Souza; Bruno Augusto Angélico; Luis Fernando Costa Alberto; Marcelo Carvalho Minhoto Teixeira

• Advisor: Cecília de Freitas Morais; Pedro Luis Dias Peres

Abstract

This thesis investigates the class of positive linear systems, that is, systems whose state variables assume only non-negative values. The main contributions of this study concern the elaboration of methods for stability analysis and for the synthesis of controllers and filters for positive linear systems. The proposed conditions are given in terms of linear matrix inequalities since, in the synthesis procedures, some variables are fixed, which leads to the construction of iterative algorithms to solve the problems. In analysis, precisely known systems (without uncertainties) are considered with saturation in the actuators, exploring the representation of saturation in terms of a ramp function and making use of relaxations of copositivity of quadratic forms in global stability conditions. The H-2 control design is addressed for continuous-time positive linear systems with uncertain parameters belonging to a polytope. In the full order dynamic output-feedback control design, positive linear systems with interval uncertainties are treated, considering continuous- and discrete-timemodels. The reduced-order H-2 and H-infinity positive filter design is investigated for positive uncertain discrete-time linear systems. The control synthesis is addressed by iterative algorithms whose main advantage is to present the conditions of the optimization problem with the Lyapunov matrix and other decision variables appearing in an affine way. This characteristic is especially advantageous in the context of positive systems, since the restrictions related to positivity can be imposed directly on the design variables (matrices of the filter or controller). Finally, the effectiveness of the proposed methods is illustrated by numerical examples (AU)

• FAPESP's process: 19/09363-5 - Control of uncertain positive linear systems by means of linear matrix inequalities
• Grantee: Amanda Spagolla
• Support Opportunities: Scholarships in Brazil - Doctorate