Identification of LFT Structured Descriptor Systems With Slow and Nonuniform Sampling

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 non-uniform and slow, in the sense that it is not required to satisfy the Nyquist frequency restrictions. This model can be used to described the behaviors of a networked dynamic system, and the obtained results can be straightforwardly applied to a standard 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 a signal generated by another system. 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 time-domain 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.