Abstract
In the identification problem of linear dynamical systems whose states can not be measured directly, the estimated values of parameters do not always converge to the true ones. One of the reasons is that the system considered is not a minimal machine and that there exist systems which are equivalent to the original systems. In this connection, p-stochastic equivalence and stochastic equivalence of dynamical systems are defined and its necessary-sufficient conditions are obtained for linear dynamical systems.
On the other hand, an algorithm of identification of linear dynamical systems using random test input and a least mean square type stochastic approximation is derived and in this algorithm, some conditions by which parameters of the system are identified uniquely are discussed with relation to the conditions of stochastic equivalence.
