On strong stabilizability of MIMO infinite-dimensional systems

Abstract

The strong stabilization problem, i.e., the problem of designing a real stable stabilizing controller, is considered for multi-input multi-output infinite-dimensional real linear systems. The considered systems may have infinitely many poles and zeros in the open right-half-plane, as well as on the imaginary axis. It is shown that the well-known parity interlacing property (pip) for real-rational systems is also a necessary condition in the most general case as long as the plant has coprime factorizations over H-infinity. which is a necessary condition for stabilizability. Furthermore, it is shown that pip is also sufficient under some additional mild assumptions. (C) 2020 Elsevier Ltd. All rights reserved.