ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - July 2012 - Volume 18, Issue 03  

Research Article

Stability of retarded systems with slowly varying coefficient

Michael Iosif Gil

Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel. gilmi@bezeqint.net

Abstract

The “freezing” method for ordinary differential equations is extended to multivariable retarded systems with distributed delays and slowly varying coefficients. Explicit stability conditions are derived. The main tool of the paper is a combined usage of the generalized Bohl-Perron principle and norm estimates for the fundamental solutions of the considered equations.

(Received February 10 2011)

(Revised July 8 2011)

(Online publication September 27 2011)

Key Words:

  • Linear retarded systems;
  • stability;
  • generalized Bohl-Perron principle

Mathematics Subject Classification:

  • 34K20