The Construction of Minimal Realizations
In this chapter we consider the problem of constructing minimal realizations. The starting point is the statement of a necessary and sufficient condition for an infinite sequence of Volterra kernels to admit a finite dimensional, constant, bilinear realization. This criterion essentially consists in a sort of “factorizability condition” of the family of kernels. Then we propose two alternative methods for constructing minimal bilinear realizations. Both these methods are based on the assumption that the abovementioned realizability condition is satisfied and operate in two steps: a first one for constructing the “factors” of the given sequence and a second for constructing, from these latter, the minimal realizations.
KeywordsRealizability Condition Bilinear System Volterra Series Minimal Realization Volterra Kernel
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