Guaranteed cost and positive real control of uncertain systems via static output feedback

This paper focuses on the problem of guaranteed cost and positive real control for a class of linear systems which are subjected to mixed structured bounded uncertainty and unbounded unknown nonlinearities in the state equation. Sufficient conditions in terms of linear matrix inequalities (LMIs) and linear matrix equalities (LMEs) are presented for the existence of a static output feedback controller, that makes the resulting closed-loop system quadratically strict positive real and minimizes the upper bound for a given cost function. A numerical example is included to illustrate effectiveness of the theoretic results obtained.Yuanqing Xia and Jie Chen, Peng Shi, Guoping Liu and David Ree