Robust dichotomy and controller design for a class of nonlinear systems

This paper focuses on the dichotomy of a class of nonlinear systems with norm-bounded parameter uncertainties. The analysis and synthesis problems of the robust dichotomous behavior are proposed for such systems. Based on Kalman-Yakubovich-Popov (KYP), sufficient conditions for robust dichotomy are derived in terms of linear matrix inequalities (LMIs). Furthermore, static state feedback controller and dynamic output feedback controller are designed such that the resulting closed-loop system is dichotomous for all admissible uncertainties. It is shown that the dynamic output feedback controller can be obtained through the static feedback controller for a new higher-order system. Moreover, it is also proven that if there exist dynamic output feedback controller such that the corresponding closed-loop system is dichotomous, there is also a static state feedback controller to realize the same purpose. Chua´s circuit and extended Chua´s circuit are studied to illustrate the theoretical results.