Quadratic Constraints for Local Stability Analysis of Quadratic Systems

TL;DR

This paper introduces novel quadratic constraints that improve the accuracy of local stability analysis for quadratic systems by reducing conservatism and utilizing sign-indefiniteness properties.

Contribution

The paper presents new quadratic constraints that tighten bounds on quadratic polynomials, enhancing stability analysis of nonlinear quadratic vector fields.

Findings

New quadratic constraints provide tighter bounds.

Numerical examples demonstrate improved local stability analysis.

Reduced conservatism compared to previous quadratic constraints.

Abstract

This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed QCs utilize the sign-indefiniteness of certain classes of quadratic polynomials. These new QCs provide a tight bound on the quadratic terms along specific directions. This reduces the conservatism of the QC bounds as compared to the QCs in previous work. Two numerical examples of local stability analysis are provided to demonstrate the effectiveness of the proposed QCs.