## Approximating Properties of Linear Models for Input-output Descriptions, Volume 1319 |

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### Contents

INTRODUCTION | 1 |

REPRESENTATION OF PADE APPROXIMANT BY DETERMINANTS | 52 |

MINIMAL REIAIZATIONS OF LINEAR DYNAMICAL SYSTEMS | 78 |

3 other sections not shown

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### Common terms and phrases

aj-i+l aj-i+2 algorithm 4.13 approximant for f approximating properties Chapter coefficients column space companion matrix completes the proof Conclusion Corollary 2.8 cr(f definition deg Q denominator polynomial dim F dimension E-array equations exists f is normal formal power series Hankel matrices HF^G Ho's algorithm hypothesis implies k=m+l l)th column Lemma linear dynamical systems linear model linear recursion linearly dependent matrices satisfying 4.2 matrix minimal realization model of order Moore's theorem necessary and sufficient nonnegative integers nonsingular nonzero numerator polynomial ordered pair orthogonal p-realizable Pade approximant Pade pair pair for f pair of nonnegative pair of polynomials partial realization positive integer pr r n Proposition proved pseudo inverse rank rational function real numbers realization F relatively prime representation theorem row space scalar sequence sequence of real smallest integer solution subspace Suppose table for f Theorem 2.5 transfer function unique zero zi+J+1