Abstract
This paper presents a method of identification for multivariable linear dynamical systems. An observable canonical form is used in this method. Generally speaking, in such a canonical representation an input-output relation can be defined in the form of the smallest number of parameters. Therefore in the case of identification the number of parameters to estimate becomes small.
This method consists of the part of Markov parameter estimation and the part of minimal realization: the parameters of an impulse response matrix which are obtained from the state equations are estimated through the least mean-square type stochastic approximation algorithm, and an observable canonical form which is controllable is derived from the formerly estimated matrix.
The proposed method has the advantage that any type of input sequence can be used for identification and that few properties of both system and observation noises need to be known.
In this paper, we deduce some equations to obtain the parameters of an observable canonical form from an impulse response matrix and also show the condition to obtain unique solutions in this case.
