Controle de sistemas lineares com saltos Markovianos e cadeia oculta usando desigualdades matriciais lineares

Abstract

This dissertation addresses the problem of designing controllers for discrete-time Markov jump linear systems, in a scenario of partial information of the Markov chain. We consider a hidden Markov model, for which we assume that the mode of operation of the system is not available to the controller, but only an estimate provided by a detector. In this context, we initially investigate the state-feedback control problem and propose sufficient conditions for the synthesis of controllers that ensure upper bounds for the performance indices H2, H∞, and ℓ2−ℓ∞. In a second moment, we address the problem of designing static output feedback controllers, and propose sufficient conditions in the context of H2, H∞ and mixed H2/H∞ control. Considering that the synthesis conditions are proposed in terms of bilinear matrix inequalities, we present an iterative approach based on a coordinated descent algorithm to obtain suboptimal solutions. The steps of the algorithm are characterized by the solution of linear matrix inequalities that guarantee a non-increasing sequence for the upper bounds of the performance indices addressed. Numerical examples are presented to illustrate the effectiveness of the results obtained, comparing them with existing methods in the literature.