Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment

Global exponential stability is the most desirable stability property of recurrent neural networks. The paper presents new results for recurrent neural networks applied to online computation of feedback gains of linear time-invariant multivariable systems via pole assignment. The theoretical analysis focuses on the global exponential stability, convergence rates, and selection of design parameters. The theoretical results are further substantiated by simulation results conducted for synthesizing linear feedback control systems with different specifications and design requirements.

I. Introduction

A PROBLEM of major importance in control applications is the synthesis of linear feedback control systems via pole assignment. As known, when all of the state variables of a time-invariant system are completely controllable and measurable, the closed-loop poles of the system can be placed at any desired locations on the complex plane with state feedback through appropriate gains [15]. Since the performance of a feedback control system is mainly determined by its closed-loop poles, pole assignment has been a very effective approach to designing feedback control systems for decades, especially for multivariate systems.