Stable Approximation of Unstable Transfer Function Models

The result of a system identification experiment is usually a parametric continuous-time (s-domain) or discrete-time (z-domain) model. Due to noise on the measurements and/or nonlinear distortions, this model can be unstable. If an additional delay is added to the unstable system, then experience shows that a stable approximation with small approximation error can be obtained. In this paper, a new numerical algorithm is proposed for finding a delay that gives a stable result. Contrary to classical approaches, it needs fewer gradientlike steps during the approximation process.