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

Abstract

An algorithm based on Linear Matrix Inequalities (LMIs) is proposed to find 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 greater than or equal to the number of its input variables. Considering that SPR systems with static output feedback are related to SPR systems with static state feedback, as shown in this manuscript, the first step of the algorithm is to find a matrix F such that all transmission zeros of the system {A,B,FC} have negative real parts. After finding this matrix F, an output feedback matrix Ko such that the system {A−BKoC,B,FC} is SPR is found. Another algorithm is proposed to specify a decay rate. The results are applied to the simulation of electrical stimulation for paraplegic patients, to vary knee joint angle from 0° to 60°.