Observability and Observer Design for Switched Linear Systems Application to Multicellular Converters

Abstract

Switching systems are systems comprising a set of continuous dynamics orchestrated by a switching signal. This important class of hybrid dynamic systems have witnessed remarkable developments from theoretical point of view to practical insights with potential benefits to many real world applications such as: power electronics, multi-controller systems, robotics, electromechanical systems and systems with discontinuities. As a result, the development of tools allowing analyze the dynamic properties such as observability and observer design represents a challenging issue notably in the case where the subsystems(modes) are unobservable in classical sense. The contribution of this thesis is divided into two parts. The first part provides, in one hand, the observability condition of the switched linear system .On the other hand, a strategy for the discrete and continuous states estimation for linear switched system including unobservable modes. This problem has been addressed using two algebraic observers. The first one estimated the actif mode. The second one, estimate the contiunous state . This strategy is based on the recent robust algebraic derivative estimation technique. Take into account the partial observability of the continuous state, the algebraic observer reconstructs the states using the output measurement and their derivatives estimation. The proposed observer provides better and fast estimation in real time. The second part of this thesis, is dedicated to the validation of the theoretical approaches for the observation of floating voltages of the multicell converter. Simulation results of two and three-cells converter confirm the theoretical results and show the effectiveness and the robustness of the hybrid observer in spite of load and input variations.