Delay dependent stability of linear time-delay systems

Abstract

This paper deals with the problem of delay dependent stability for both ordinary and large-scale time-delay systems. Some necessary and sufficient conditions for delay-dependent asymptotic stability of continuous and discrete linear time-delay systems are derived. These results have been extended to the large-scale time-delay systems covering the cases of two and multiple existing subsystems. The delay-dependent criteria are derived by Lyapunov's direct method and are exclusively based on the solvents of particular matrix equation and Lyapunov equation for non-delay systems. Obtained stability conditions do not possess conservatism. Numerical examples have been worked out to show the applicability of results derived. [Projekat Ministarstva nauke Republike Srbije, br. ON174001: Dynamics of hybrid systems with complex structures]

Keywords

• continuous time-delay systems
• discrete time-delay systems
• large-scale time-delay systems
• delay-dependent stability
• Lyapunov stability
• necessary and sufficient conditions