Strictly negative imaginary state feedback control with a prescribed degree of stability

This paper presents conditions for the synthesis of a strictly negative imaginary closed-loop system with a prescribed degree of stability under the assumption of full state feedback. A perturbation method is used to ensure the closed-loop system has both the strict negative imaginary property and a prescribed degree of stability. This approach involves the real Schur decomposition of a matrix followed by the solution to two Lyapunov equations. Also, we present and clarify the perturbation properties of strictly negative imaginary systems.