Estabilidade e síntese de controladores e filtros robustos para sistemas com retardo no tempo: novas fronteiras

Abstract

This thesis is dedicated to the study of some inherent problems in continuous-time systems with time delay. The thesis is divided into two parts; the first one shows that to study the stability of an autonomous linear system with constant time delay is equivalent to assess the roots of a rational function of appopriate degree. The second part deals with a set of stability analysis methods, based on linear matrix inequalities (LMIs), for continuous-time systems, uncertain, linear and non-linear, subject to time delay. It is also proposed a systematic way to extend the new stability tests for synthesis of robust controllers and filters, which can include H-infinity performance. The methodology used in this second part makes use of appropriate selections of Lyapunov-Krasovskii functionals, a strategy of discretization and matrix relaxations. Several computer simulations are presented throughout the thesis and compared with other recent approaches in the literature, which corroborate the efficiency of the proposed results.