An observer-based control scheme using negative-imaginary theory

This paper presents a full-order state observer-based scheme that transforms a causal, LTI, minimally realized system into a strongly strict negative-imaginary system by defining an auxiliary output based on the observed states. The auxiliary output is used for closed-loop control with positive feedback invoking the internal stability condition of negative-imaginary theory. A set of LMI conditions is derived that determines the value of a design parameter μ required for the proposed scheme to transform a given system with a minimal state-space realization into a strongly strict negative-imaginary system. The proposed scheme is applicable for both stable/unstable and square/non-square systems. In this paper, the framework is further explored for robustness analysis of uncertain systems and numerical examples are given to elucidate effectiveness of the proposed results.