Identification of LFT Structured Descriptor Systems with Slow and Non-uniform Sampling

TL;DR

This paper develops a method for identifying parameters of continuous-time descriptor systems from slow, non-uniform sampled data without Nyquist restrictions, applicable to networked systems and providing explicit response formulas.

Contribution

It introduces a novel identification approach for descriptor systems under slow, irregular sampling, with explicit formulas and estimation algorithms analyzed for their properties.

Findings

Explicit formulas for transient and steady-state responses.

Estimation algorithms for system parameters and transfer function matrix.

Algorithms shown to be asymptotically unbiased and consistent.

Abstract

Time domain identification is studied in this paper for parameters of a continuous-time multi-input multi-output descriptor system, with these parameters affecting system matrices through a linear fractional transformation. Sampling is permitted to be slow and non-uniform, and there are no necessities to satisfy the Nyquist frequency restrictions. This model can be used to describe the behaviors of a networked dynamic system, and the obtained results can be straightforwardly applied to an ordinary state-space model, as well as a lumped system. An explicit formula is obtained respectively for the transient and steady-state responses of the system stimulated by an arbitrary signal. Some relations have been derived between the system steady-state response and its transfer function matrix (TFM), which reveal that the value of a TFM at almost any interested point, as well as its derivatives and a right tangential interpolation along an arbitrary direction, can in principle be estimated from input-output experimental data. Based on these relations, an estimation algorithm is suggested respectively for the parameters of the descriptor system and the values of its TFM. Their properties like asymptotic unbiasedness, consistency, etc., are analyzed. A simple numerical example is included to illustrate characteristics of the suggested estimation algorithms.