Linear Systems

A frequency-domain criterion for the quadratic stability of discrete-time systems with switching between three linear subsystems

V.A.Kamenetskiy

V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow

Abstract: Connected systems with switching between three linear discrete-time subsystems are considered, and a new frequency-domain criterion for the existence of a quadratic Lyapunov function ensuring the stability of such systems under arbitrary switching is proposed. The application of this criterion is demonstrated on an example of a third-order system.

Keywords: discrete-time switched systems, stability, Lyapunov functions, matrix inequalities.

Presented by the member of Editorial Board: P. V. Pakshin

Received: 14.03.2024
Revised: 21.05.2024
Accepted: 30.05.2024

DOI: 10.31857/S0005231024070014

 English version: Automation and Remote Control, 2024, 85:7, 575–583