Analytic criteria for the stability of linear control systems with time delay

Abstract

AbstractThe influence of time delay in linear control systems is often modeled by approximations. Here analytic criteria for determining the stability of linear differential delay systems are described. The characteristic function of such a system is a quasipolynomial, i.e. a polynomial Q(z) multiplied by powers of the exponential function exp(‐τz) plus another polynomial P(z). Using concepts of the theory of functions it has been shown that by evaluating a sequence of path integrals or the integral over the derivative of the logarithm of the characteristic function along the positive part of the imaginary axis it can be determined if the system is stable. As new result it is derived that by estimating the maximal modulus of the zeros of the characteristic function this can be reduced to the calculation of a path integral of this function over a finite contour.