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Hankel-matrix approach to invertibility of linear multivariable systems. (English) Zbl 0536.93016
Summary: The transfer-function matrix R(s) of a linear multivariable system can be represented by the matrix fraction description \(R(s)=P(s)Q^{- 1}(s)=\tilde Q^{-1}(s)\tilde P(s)\) or by \(R(s)=\bar P(s)/q(s)\) where q(s) is the common denominator of all entries in R(s). Based on either of these descriptions, new criteria of k-integral invertibility of linear multivariable systems are derived which are expressed as a rank condition of matrices formed by the parameters in the numerator matrix P(s) (or \(\tilde P\)(s) or \=P(s)) and denominator matrix Q(s) (or \(\tilde Q\)(s) or the denominator polynomial q(s)). A new method based on the Hankel-matrix is used to construct the inverse, to parametrize the set of all minimal order inverses and to identify the stable minimal inverse if it exists.

MSC:
93B25 Algebraic methods
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
15A03 Vector spaces, linear dependence, rank, lineability
15A23 Factorization of matrices
15A09 Theory of matrix inversion and generalized inverses
93B15 Realizations from input-output data
93B20 Minimal systems representations
93C99 Model systems in control theory
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