An algebraic approach for delay-independent and delay-dependent stability of linear time-delay systems

This paper addresses the problem of asymptotic stability of a linear system with many delay units. A novel algebraic test is proposed for the delay-independent stability of the system, based on the root distribution of the system´s characteristic equation. If the system is only stable dependent of delay, the whole stable regions of the system can be perfectly obtained. Two algorithms are derived to examine the delay-independent stability, and to compute the whole stable regions if the system is of delay-dependent stability. These algorithms are computationally efficient and applicable to both certain and uncertain systems. Some illustrative examples demonstrate the validity of the approach.