Stability of Networked Systems with Multiple Delays Using Linear Programming

In this paper, we present a new sufficient stability condition for linear time-invariant multiple time-delay systems (MTDS) based on the Rekasius substitution and linear programming. The main advantage of the new stability condition is that it is applicable to the general case of multiple, incommensurate delays yet numerically tractable. In particular, using efficient linear programming algorithms, a numerical stability test is derived to determine a maximum delay tau macr macr such that the system is stable for all delays tau_k with tau_k les tau macr.