Local passivity analysis of nonlinear systems: A sum-of-squares optimization approach

This paper deals with the problem of passivity and passivity indices in nonlinear systems. Since the behavior of nonlinear systems depends on the neighborhood of interest, a local approach is taken to study passivity and passivity indices of such systems. An optimization-based method for passivity analysis of nonlinear systems is presented here. The system's dynamics are considered to be defined by polynomial functions, which can cover a broad range of nonlinear systems. Also, state space and input space are considered to be defined as semialgebraic sets. Results are presented as sum of squares optimization, which can directly address nonlinearities without any linearization or further approximation. Examples are given to show the necessity of local analysis for passivity of nonlinear systems and demonstrate the effectiveness of the proposed method.