Exact Instability Margin Analysis and Minimum-Norm Strong Stabilization -- phase change rate maximization --

Abstract

This paper is concerned with a new optimization problem named "phase change rate maximization" for single-input-single-output linear time-invariant systems. The problem relates to two control problems, namely robust instability analysis against stable perturbations and minimum-norm strong stabilization. We define an index of the instability margin called "robust instability radius (RIR)" as the smallest $H_{\infty }$-norm of a stable perturbation that stabilizes a given unstable system. This paper has two main contributions. It is first shown that the problem of finding the exact RIR via the small-gain condition can be transformed into the problem of maximizing the phase change rate at the peak frequency with a phase constraint. Then, we show that the maximum is attained by a constant or a first-order all-pass function and derive conditions, under which the RIR can be exactly characterized, in terms of the phase change rate. Two practical applications are provided to illustrate the utility of our results.

References in corpus (4)

• Instability Margin Analysis for Parametrized LTI Systems with Application to Repressilator
• Robust Instability Analysis with Application to Neuronal Dynamics
• Exact Instability Margin Analysis and Minimum-Norm Strong Stabilization -- phase change rate maximization --
• On Phase Change Rate Maximization with Practical Applications

Cited by in corpus (1)

• Exact Instability Margin Analysis and Minimum-Norm Strong Stabilization -- phase change rate maximization --