Robust strict positive realness synthesis for uncertainty systems with LMI approach

This paper is devoted to synthesizing a stabilizing feedback controller for a linear time-invariant plant with norm-bounded uncertain coefficient matrices so that the corresponding closed-loop system is robustly strictly positive real. Quadratic strict positive real system is defined first. Necessary and sufficient conditions for the system are then established. Finally, state-space formulas for the state feedback controller are given in terms of solutions to linear matrix inequalities. The feasibility of the proposed method is confirmed by a numerical example.