Stability analysis of linear systems with time-varying delays Delay uncertainty and quenching

Silviu-Iulian Niculescu (1) , Antonis Papachristodoulou (2) , Matthew A. Peet (3)

1 L2S - Laboratoire des signaux et systèmes
2 University of Oxford
3 INRIA Rocquencourt

This paper addresses the problem of stability analysis of a class of linear systems with time-varying delays. We develop conditions for robust stability that can be tested using Semidefinite Programming using the Sum of Squares decomposition of multivariate polynomials and the Lyapunov-Krasovskii theorem. We show how appropriate Lyapunov-Krasovskii functionals can be constructed algorithmically to prove stability of linear systems with a variation in delay, by using bounds on the size and rate of change of the delay. We also explore the quenching phenomenon, a term used to describe the difference in behaviour between a system with fixed delay and one whose delay varies with time. Numerical examples illustrate changes in the stability window as a function of the bound on the rate of change of delay.

Domaines: Automatique

Silviu-Iulian Niculescu, Antonis Papachristodoulou, Matthew A. Peet. Stability analysis of linear systems with time-varying delays Delay uncertainty and quenching. 46th IEEE Conference on Decision and Control, Dec 2007, New Orleans, United States. ⟨hal-02194457⟩