Doğrusal olmayan ve anahtarlamalı sistemler için gözlenebilirlik ve gözleyiciler

ABSTRACT OBSERVABILITY AND OBSERVERS FOR NONLINEAR AND SWITCHING SYSTEMS - > Ercan Solak Ph.D. in Department of Electrical and Electronics Engineering Supervisor: Prof. Dr. Ömer Morgül August 2001 One of the fundamental problems in control theory is the observability and observer construction for nonlinear systems. In this thesis we study the observability conditions for some classes of nonlinear and switching systems and related observer design methods. We adapt and modify high-gain observers to suit their application to observer-based chaos synchronization, control and tracking. We show that stringent global conditions on the system structure can be relaxed for chaotic systems. Using the close relation between chaos synchronization and observers, we provide chaotic message encoding schemes that incorporate exponential observers with robust message reconstruction properties. We also provide an eigenvalue assignment procedure to reduce gains and transient overshoots in high-gain observers for systems in Brunowsky canonical form. For the observability of discrete-time switching systems, we give an equivalence relation for the case of periodic switching, which in turn is used in observer construction. In the more general setting, we formulate the observability of switching systems as a feasibility problem and provide a recursive algorithm to determine the observability of a linear switching system. The algorithm relies on the recursive reduction of indistinguishable sets. We also prove some ivsufficiency conditions on the stability of switching systems, extending the stable classes provided by some existing results in the field. Relation between stability for arbitrary switching and the existence of norms defined by non-trivial convex sets is also shown. Keywords: Observability, Observers, Chaos synchronization, Chaotic encoding, Switch ing systems, Periodic switching.