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A smoothly parameterized family of stabilizable, observable linear systems containing realizations of all transfer functions of McMillan degree not exceeding n

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2 Author(s)
Pait, F.M. ; Dept. of Electr. Eng., Yale Univ., New Haven, CT, USA ; Morse, A.S.

It is shown that there is a continuously parameterized family F of n-dimensional single-input single-output (SISO) stabilizable detectable linear system Σ(p) which contains at least one realization of each reduced, strictly proper transfer function of McMillan degree not exceeding n. The parameterization map p→Σ(p) is a polynomial function in 2n indeterminates from an open convex polyhedron in R2n to the linear space of all SISO n-dimensional linear systems

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Automatic Control, IEEE Transactions on  (Volume:36 ,  Issue: 12 )