Comparison of Different Stability Conditions for Linear Time-Delay Systems with Incommensurate Delays

We compare different stability conditions for linear time-delay systems with multiple incommensurate, time-invariant delays. In total, nine sufficient stability conditions are taken from the literature and implemented in MATLAB. All of them guarantee asymptotic stability if all delays τk are smaller than a bound. The different conditions are then tested on nine examples which have served as benchmark examples in various earlier publications. The different conditions are compared with each other with respect to computational effort and maximal achievable bound, for which asymptotic stability is guaranteed.