Controller and Observer Design using Vector Framework with Simplified Contraction Analysis

This technical note presents the application of simplified contraction analysis using vector framework. In general, conventional approach leads to guaranteeing negative definiteness of the associated Jacobian for ensuring convergence of any pair of trajectories. A vector valued norm is used for simplification of the problem to ensure contraction through the comparison systems. In fact, comparison systems are used for ensuring convergence of the squared distances between any pair of trajectories in a simplified way. We show that by employing this simplified contraction analysis, it is possible to design controller and observer. The methodology is illustrated via a set of representative examples.