Control of negative imaginary systems exploiting a dissipative characterization

Abstract

This paper utilizes a dissipative framework to construct a set of stabilizing controllers in positive feedback for LTI negative imaginary (NI) systems with no pole at origin. The technique relies on identifying a dissipative characterization of such NI systems. Contrary to the existing literature, the set of controllers presented in this paper may not belong to the NI systems class and can be designed having only a rough estimate of the DC gain of the plant. Apart from extending the class of stabilizing controllers beyond the NI family, the proposed framework also generalizes a few existing NI domain results. It is shown that the integral resonant control (IRC) scheme in MIMO setting can be captured as a special case of the developed result. Integral controllability of a class of NI systems having negative definite DC gain directly follows from the proposed stability result of this paper. Further generalization in terms of the set of integral gain matrix is also demonstrated. Effectiveness of the proposed results are illustrated through numerical examples.