题目: Stability of continuous-time difference equations

报告人：Guilherme MAZANTI，INRIA Saclay-île-de-France（法国国家信息与自动化研究所）

时间：2025年3月19日（星期三）16: 00-17: 00

地点：东区第五教学楼5406教室

摘要：

Continuous-time difference equations are dynamical systems in which the variable of interest x(t) is expressed as a function of x itself calculated at previous times. These equations define a class of time-delay systems, which can be seen as the simplest class of neutral-type time-delay systems. In addition to their relations to other classes of time-delay systems, the study of continuous-time difference equations is also motivated by their links to some classes of hyperbolic partial differential equations in one space dimension.

After presenting continuous-time difference equations and the motivations for their study, this talk will present classic and more recent results on their stability analysis. We will focus on the linear case, which is already rich enough and allows one to observe many interesting phenomena. We begin by presenting some classic results on the stability and stabilization of time-invariant linear difference equations, notably the Hale–Silkowski strong stability criterion. We then address the stability of linear difference equations with time-dependent parameters, showing that several results of classical theory remain valid as long as delays remain constant, but that several subtleties arise in the case of time-varying delays.

The recent results presented in this talk are based on a series of joint works with Yacine Chitour, Jaqueline Godoy Mesquita, and Mario Sigalotti.