Sensitivity function reduction through use of the Jordan canonical form

Parameter identification techniques generally require an iterative search to obtain the solution. Gradient search techniques require the integration of differential equations defining the sensitivities of the states with respect to the parameters. It has previously been shown that for linear systems substantial computational savings may be achieved by transformation to the controllable subspace. Here it is shown that: (1) transformation first to the Jordan form results in a simpler proof of the maximal dimension of the controllable subspace; (2)certain numerical difficulties of the earlier method may be largely avoided, but at the expense of assuming the problems of computing a Jordan form; and (3) the controllable subspace has a standard structure which may be defined by inspection from the Jordan form.