Stability of Networked Systems with Multiple Delays Using Linear Programming

Ulrich Münz, Christian Ebenbauer, Frank Allgöwer

Abstract: 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 τ¯ such that the system is stable for all delays τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> with τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ≤ τ¯.