Linear Program-Based Stability Conditions for Nonlinear Autonomous Systems

TL;DR

This paper presents a new linear programming-based method for assessing the stability of nonlinear autonomous systems, offering computational efficiency and scalability over traditional SDP-based techniques.

Contribution

It introduces a novel LP-based stability criterion using Jacobian linearization, replacing SDP methods for improved computational efficiency in high-dimensional systems.

Findings

Significantly reduces computational time and memory usage.

Demonstrates scalability to high-dimensional systems.

Outperforms SDP-based criteria in efficiency and applicability.

Abstract

This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing system dynamics through Jacobian matrices, the methodology replaces traditional semi-definite programming (SDP) techniques with computationally efficient linear programming (LP) conditions. This substitution substantially lowers the computational burden, including time and memory usage, particularly for high-dimensional systems. The stability criteria are developed using matrix transformations and leveraging the structural characteristics of the system, improving scalability. Several examples demonstrated the computational efficiency of the proposed approach compared to the existing SDP-based criteria, particularly for high-dimensional systems.