Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems

TL;DR

This paper presents a new Lyapunov-based proof confirming the stability of feedback interconnections in negative imaginary systems, addressing previous proof shortcomings and ensuring robust control in high-precision sensor applications.

Contribution

The paper offers a corrected Lyapunov-based proof for the stability of negative imaginary system interconnections, improving theoretical rigor in the field.

Findings

Validated the stability of feedback interconnections with the new proof

Confirmed the robustness of control design for high-precision systems

Addressed and fixed a matrix inevitability issue in previous proofs

Abstract

Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to un modelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper we provide a new and correct Lyapunobv-based proof of one such result and show that the result is still true.