Controller and Observer design for Chaotic Systems: A Vector Based Contraction Approach

A new strategy for the design of controller and state observer is proposed based on the vector based contraction framework. The methodology gives relaxation over the conventional contraction theory as there is no requirement to guarantee the negative definiteness of the complex Jacobian matrix to derive convergence results. The vector framework is used to simplify the problem through the comparison systems. Specifically, suitable choice of comparison system derives the convergence of squared distance between any pair of trajectories in a reduced way. The examples of controller design for duffing system and observer design for Chua's circuit are illustrated to see the implementation of the proposed results. Furthermore, results are observed through simulation.