Estabilidade de sistemas chaveados baseados em objetivo de controle principal.

Abstract

Nowadays, a growing interest of research groups for hybrid systems can be seen, especially for the switched systems. Due to the need to develop tools that can assist the work in this area, mainly in sense of the stability analysis, in this PhD thesis is proposed a new field of stability analysis of switched systems based on the choice of a main objective for the system. As a result of this proposal, there is the possibility that subsystems may have different points of equilibrium, or even some of them can be unstable. According to this approach, only the main subsystem needs to be globally asymptotically stable. However, when the switching is performed, the Lyapunov stability is often inappropriate, since the norm of state variables may temporarily grow for the switched systems. Thus, an alternative to Lyapunov stability is the practical stability, focused to applications, which is based on a quantitative approach. In this context, this work addresses the quasi-stable systems, which are systems that met the Lyapunov condition after a time τ. In this way, this PhD thesis proposes a definition of quasi-stable and two propositions with sufficient conditions for this kind of stability.Additionally, in this work, three propositions are presented, which should help in the stability analysis of a significant number of systems with the main control objective characteristic, including the case of nonlinear switched control. The contributions of this work are illustrated by the presentation of simulations and experimental results. These results cover the control of chemical processes and mobile robot navigation areas.