Parameter identification of continuous systems with multiple input time delays via modulating functions

The identification of continuous systems with multiple-input delays is discussed. A batch algorithm for parametric identification of both multiple time delays and unknown parameters is proposed, using the modulating function approach. If the unknown delay is expressed as a linear combination of a bank of known delays, it is proven that the distribution of the identified coefficients is a sampling centred on the unknown delays; the result is then extended to the multiple delay case. The modulating function method guarantees a continuous-time approach and robustness for a high value of noise-to-signal ratio. Simulation results are included to illustrate the proposed technique.