Model conversions of uncertain linear systems using the Pade and inverse-Pade method

The paper presents a mixed method consisting of the Pade approximation and the inverse-Pade approximation method for model conversions of a continuous-time (discrete-time) structured uncertain linear system to an equivalent discrete-time (continuous-time) structured uncertain linear model. This allows the use of well-developed theorems and algorithms in the discrete-time (continuous-time) domain to indirectly solve the continuous-time (discrete-time) domain problems. When the ratio of the uncertainties ( Delta A, Delta B) to the nominal system parameters (A₀, B₀) and/or the sampling period (T0//+// Delta A//)) are sufficiently small, the linearised uncertain models can be obtained by neglecting the nonlinear uncertain terms, O(T² Delta A²) and O(T² Delta A Delta B),in the state-space models. The comparison of a high-order Pade approximate model with the bilinear approximate model and the Taylor-series approximate model is also presented. Moreover, this paper also presents a method to estimate tighter bounds of discrete-time (continuous-time) structured uncertainties based on the given continuous-time (discrete-time) structured uncertainties.