A Necessary and Sufficient First Delay-Interval Stability Condition

This paper is concerned with stability of the first delay-interval of linear delay systems. Stability analysis of linear delay systems is complicated by the presence of exponential transcendental terms in the characteristic equation. The main result consists in showing that first delay-interval stability can be assessed by verifying the stability of an associated rational characteristic equation. A single real parameter on this associated rational characteristic equation plays the role of the time-delay in the original transcendental characteristic equation.