Accelerated Stabilization of Switched Linear MIMO Systems using Generalized Homogeneity

TL;DR

This paper introduces a generalized homogenization framework for stabilizing switched linear MIMO systems rapidly and robustly, utilizing implicit Lyapunov functions and linear matrix inequalities to achieve finite-time and nearly fixed-time stabilization.

Contribution

It presents a novel generalized homogenization approach combined with Lyapunov functions for accelerated stabilization of switched linear MIMO systems, including robustness analysis.

Findings

Effective stabilization demonstrated through numerical examples.

Framework achieves exponential and finite-time stabilization.

Robustness against uncertainties and disturbances verified.

Abstract

This paper addresses the problem of exponential and accelerated finite-time, as well as nearly fixed-time, stabilization of switched linear MIMO systems. The proposed approach relies on a generalized homogenization framework for switched linear systems and employs implicit Lyapunov functions for control design, covering both common and multiple Lyapunov function settings. Linear matrix equations and inequalities are derived to characterize the dilation generator and to synthesize the controller gains. Robustness of the resulting control laws with respect to system uncertainties and external disturbances is analyzed. The effectiveness of the proposed approach is illustrated through numerical examples.