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On negative imaginary synthesis via solutions to Riccati equations

Abstract:

This paper tackles the problem of finding conditions for the existence of an output feedback controller such that the closed-loop system becomes strictly negative imaginary (SNI) and internally stable. In order to achieve this objective, we derive a set of necessary and sufficient conditions to check the SNI property of systems with a non necessarily minimal state-space realization. Then, we propose a set of sufficient conditions for the controller synthesis problem and we also provide a formula for such controller.