On annular short-time stability conditions for generalized Persidskii systems

TL;DR

This paper introduces new stability conditions for generalized Persidskii systems, focusing on annular short-time stability and boundedness, verified through linear matrix inequalities, with applications to neural networks.

Contribution

It proposes novel annular stability and boundedness conditions for Persidskii systems using linear matrix inequalities, extending stability analysis tools.

Findings

Conditions for annular short-time stability are established.

The approach is validated through an application to recurrent neural networks.

The proposed conditions facilitate stability analysis of nonlinear systems.

Abstract

This paper studies the trajectory behavior evaluation for generalized Persidskii systems with an essentially bounded input on a finite time interval. Also, the notions of annular settling and output annular settling for general nonlinear systems are introduced. We propose conditions for annular short-time stability, short-time boundedness with a nonzero initial state, annular settling, and output annular settling for a class of Persidskii systems. These conditions are based on the verification of linear matrix inequalities. An application to recurrent neural networks illustrates the usefulness of the proposed notions and conditions.