Convex parametrization of H∞ controllers for positively dominated systems

This work presents a convex parametrization of H∞ output feedback controllers for positively dominated systems. The objective is to design static and dynamic output feedback controllers such that the closed-loop system is positively dominated, asymptotically stable and the H∞ norm from the exogenous input to the regulated output is minimized. By utilizing Youla parametrization, the stabilizing controllers which give rise to a positively dominated system is parameterized by Q-parameters and extended to design static and dynamic H∞ output feedback controllers through semi-definite programming (SDP). Due to the versatility of the presented framework for positively dominate systems, the design is extended to robust performance scenarios with structured and unstructured norm-bounded uncertainties.