Robust Stability Test for Dynamic Systems with Short Delays by Using Padé Approximation

Abstract

The paper presents a simple approach to testifying the asymptotic stability and interval stability (robust stability against the change of system parameters in given intervals) for linear dynamic systems involving short time delays. The stability analysis starts with the study of the characteristic roots of a transcendental equation having exponential functions. By means of the Pade approximation to the exponential functions, the transcendental characteristic equation is approximated as an algebraic equation. Then, the test of asymptotic stability and interval stability of the system is completed in a very simple way. The stability analysis of a vibration system with short time delays in the feedback paths of displacement and velocity, taken as an example, is given in detail. The analysis and numerical examples indicate that the approach gives excellent accuracy for linear dynamic systems with short time delays.