Robust stabilization of marginally stable positive-real systems

This paper investigates the stability of the negative feedback interconnection to two positive-real systems which have poles in the closed left-half of the complex plane. A new definition of marginally strict positive real systems is introduced, and sufficient conditions are obtained for the stability of the feedback interconnection of such systems, using the Lyapunov method. The conditions obtained have direct applications to dynamic dissipative controllers for flexible spacecraft and are the least restrictive ones published to date.