Analysis, design and application of nonlinear observer and chaos synchronization

This dissertation focuses on nonlinear observer design and its application in chaos synchronization. We consider a class of nonlinear systems that can be transformed into Linear Parameter Varying (LPV) forms via linearization and/or coordinate transformation methods. For this class of systems we present a general observer structure and solve the observer design problem using the popular "gain scheduling" technique. We show that the observer state converges to that of the true plant, provided that the deviation between the plant model and the LPV form is locally bounded.;Finally, circuit realizations are presented and simulated using state-of-the-art circuit simulation techniques. The results confirm the effectiveness of our approach.;After solving the observer problem we consider the chaos synchronization problem. We show that a large class of systems, denoted "Quadratic Chaotic Systems" (QCSs) that exhibit chaotic dynamics, can be exactly modeled in LPV form. For this class we propose two different synchronization structures and solve the synthesis problem using the gain scheduling approach. We also study the effect of modeling errors and time delays in the synchronization methods and formulate procedures that extend the two synchronization methods to account for both parametric uncertainties and channel time delay.