Identification of linear systems containing unknown gain elements

We consider the identification of stable linear systems is which all but a limited number of parameter values (usually physical in origin) are known. Such parameter values may correspond to mass, friction coefficient, reaction rate constant, mutual inductance, etc. Using a characterization of the output error between the true system and a model of it containing adjustable parameters, we describe a recursive algorithm for estimating the unknown parameter value. A persistency of excitation condition on the input is described which ensures a local convergence property for the algorithm.