Stability analysis and stabilization of systems with hyperexponential rates

TL;DR

This paper investigates hyperexponential stability in dynamical systems, proposing a nonlinear control method designed via LMI, which shows improved robustness and performance over finite-time controls through theoretical and numerical validation.

Contribution

It introduces a novel hyperexponential control for linear systems with a formal LMI-based tuning procedure, enhancing robustness against noise, discretization, and delays.

Findings

Hyperexponential control is less sensitive to noise and discretization errors.

The proposed control outperforms finite-time analogs in delay robustness.

Theoretical results are validated through numerical simulations.

Abstract

Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure is formalized in LMI form. Through numeric experiments, it is observed that the proposed hyperexponential control is less sensitive with respect to noises and discretization errors than its finite-time analog. It also demonstrates better performance in the presence of delays as well. Theoretical results are supported by numerical simulations.