Further results on finite time and practical stability of linear continuous time delay systems

Abstract

In this paper, finite-time stability and practical stability problems for a class of linear continuous time-delay systems are studied. Based on the Lyapunov-like functions, that do not have to be positive definite in the whole state space and not need to have negative definite derivatives along the system trajectories, the new sufficient finite-time stability conditions are obtained. To obtain the conditions for attractive practical stability, the mentioned approach is combined with classical Lyapunov technique to guarantee attractivity properties of system behavior, and new delay dependent sufficient condition has been derived. The described approach was compared with some previous methods and it has been showed that the results derived are commonly adequate but easier for numerical treatment.

Keywords

• linear continuous system
• time-delay
• finite-time stability
• practical stability
• lyapunov function