Robustness of linear systems by means of linear matrix inequalities relaxations

Author(s)

Ricardo Coração de Leão Fontoura de Oliveira

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2006-03-24

Examining board members

Pedro Luis Dias Peres; Vinicius Foletto Montagner; João Manoel Gomes da Silva Jr.; Paulo Augusto Valente Ferreira; Ricardo Hiroshi Caldeira Takahashi

• Advisor: Pedro Luis Dias Peres

Abstract

This thesis proposes, as main contribution, a new methodology to solve parameterdependent linear matrix inequalities which frequently appear in robust analysis and control problems of linear system with polytopic uncertainties. The proposed method relies on the parametrization of the solutions in terms of homogeneous polynomials of arbitrary degree with matrix valued coefficients. For constructing such solutions, a procedure based on optimization problems formulated in terms of a finite number of linear matrix inequalities is proposed, yielding sequences of relaxations which converge to a homogeneous polynomial solution whenever a solution exists. Problems of robust analysis and guaranteed costs are analyzed in details for continuous and discrete-time uncertain systems. Several numerical examples are presented illustrating the efficiency of the proposed methods in terms of accuracy and computational burden when compared to other methods from the literature (AU)