On LMI-based algorithm for strictly positive real systems with static output feedback

This paper presents a new theoretical analyses and a condition regarding to an algorithm, based on Linear Matrix Inequalities (LMIs), for finding a constant output feedback matrix Ko and a constant output tandem matrix F such that the controlled system {A-BKoC,B, FC} is Strictly Positive Real (SPR). The number of output variables of the plant {A,B,C} is supposed to be greater than or equal to the number of its input variables. The main result offers a more general necessary condition to specify the matrix F that can offer a solution for this problem, that works when a known condition holds and also in some cases where this known solution does not hold. A numerical example illustrates the effectiveness of this procedure and its application in the design of output variable structure controllers.