Análise e síntese de controladores e filtros robustos para sistemas com domínios politópicos de incerteza

Abstract

This thesis proposes new strategies for analysis and synthesis of robust H2/H-infinity systems with regional pole placement, considering linear time-invariant systems with polytopic uncertainty domains. The proposed robust stability analysis approach combines linear matrix inequality (LMI) sufficient conditions and a polytope partition strategy. The proposed performance analysis approach is based on the combination of a branch-and-bound algorithm and LMI analysis formulations allowing the computation of the H2 or H-infinity costs with any required accuracy. The proposed synthesis approach is based on an optimization problem where the controller, filter, or reduced model parameters are the optimization variables and the design objetives as well the constraints are verified in a finite set of points initialized with the polytope vertex set, with the iterative inclusion, when necessary, of interior points. The design is validated for the whole polytope by means of the proposed analysis approaches. The aim of this work is to seek for a design approach that provides less conservative solutions or even consider performance/structural constraints that are not handled by means of LMI formulations or are not feasible. The synthesis procedure is applied to several controller, filter, and model reduction problems achieving improved or the same performance than other strategies.