Delay-dependent stability analysis of neutral systems using positive polynomials optimization

The main goal of this paper is to investigate the stability of neutral systems, by using some features of the method introduced by Zhang, Knospe and Tsiotras Zhang et al. (2003) for the standard time-delay case. The central idea consists in replacing the delay by some appropriate Padé approximation, obtaining a (sufficient) delay-dependent stability condition for the neutral system. Such a condition can be rewritten as a positivity constraint on a twovariable matrix polynomial, leading to an effective computation of the delay margin by using sum-of-squares representations of multivariable positive matrix polynomials.