Polynomial Matrices and Matrix Fraction Descriptions

David F. Delchamps
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David F. Delchamps: Cornell University, School of Electrical Engineering

Chapter 22 in State Space and Input-Output Linear Systems, 1998, pp 289-321 from Springer

Abstract: Abstract In §21, we discovered (c.f. Theorem 21.9) that a real m-input, p -output time-invariant continuous- or discrete-time input-output linear system with impulse response t → H(t) or k → H(k) was realizable if and only if its transfer function s → G (s) or z → G (z) agreed on its region of convergence ROC(H) with a real proper (p × m) matrix rational function of s or of z. The constant realizations for such a system was shown in Facts 21.10 to lie in one-to-one correspondence with matrix quadruples (A, B, C, D) which satisfied $$\begin{aligned} & & & G\left( s \right) = C{\left( {s{I_n} - A} \right)^{ - 1}}B + D,\quad s \in ROC\left( H \right), \\ or \\ G\left( z \right) = C{\left( {z{I_n} - A} \right)^{ - 1}}B + D,\quad z \in ROC\left( H \right). \\ \end{aligned} $$

Date: 1998
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DOI: 10.1007/978-1-4612-3816-4_23

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