Identification of deterministic time-lag systems

The methods of system identification due to Shinbrot, Perdreauville and Goodson, Fairman and Shen, and Diamessis belong to a class of techniques based on the idea that a linear operation on system equations leads to a set of simultaneous equations solvable for the unknown parameters. These methods have so far been able to treat problems of linear time invariant, time-varying, nonlinear, and distributed parameter systems without lags. This short paper extends the capability of the class of methods to cover time-lag systems. The extension is illustrated with reference to one of the methods that employs Poisson moment functionals. Illustrative examples include linear time invariant, time-varying, and non-linear systems each with a lag.