On the uniform exponential stability of a wide class of linear time-delay systems

• Published in: Journal of mathematical analysis and applications Vol. 289; no. 2; pp. 456 - 476
• Main Authors: De la Sen, M., Luo, Ningsu
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 15.01.2004; Elsevier
• Subjects: Exact sciences and technology; Integral equations; Mathematical analysis; Mathematics; Ordinary differential equations; Sciences and techniques of general use; Stability; Stabilization; Time-delay systems; Time-delay systems; Stabilization; Stability; Solution uniqueness; Initial condition; Differential equation; Feedback regulation; Inverse transformation; Delay equation; Exponential function; Linear operator; Delay time; Laplace transformation; Integrodifferential equation; Volterra equation
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2003.08.048

This paper deals with the global uniform exponential stability independent of delay of time-delay linear and time-invariant systems subject to point and distributed delays for the initial conditions being continuous real functions except possibly on a set of zero measure of bounded discontinuities. It is assumed that the delay-free system as well as an auxiliary one are globally uniformly exponentially stable and globally uniform exponential stability independent of delay, respectively. The auxiliary system is typically a part of the overall dynamics of the delayed system but not necessarily the isolated undelayed dynamics as usually assumed in the literature. Since there is a great freedom in setting such an auxiliary system, the obtained stability conditions are very useful in a wide class of practical applications.