We present a new stability condition for linear time-delay systems (TDS) with multiple incommensurate delays based on the Rekasius substitution and positive polynomials. The condition is checked by testing the positivity of multivariate polynomials in certain domains. For this purpose, we propose two alternative algorithms based on linear programming and sum of squares methods, respectively. The efficiency and accuracy of the algorithms is compared in an example to alternative stability conditions taken from the literature.
['Ulrich Münz', 'Christian Ebenbauer', 'Thomas Haag', 'Frank Allgöwer']
Stability Analysis of Time-Delay Systems With Incommensurate Delays Using Positive Polynomials