## Linear multivariable control: algebraic analysis and synthesis methodsDetails the basic theory of polynomial and fractional representation methods for algebraic analysis and synthesis of linear multivariable control systems. It also serves as a self-contained treatise of the mathematical theory so that results and techniques of the ``state space approaches'' for regular and singular systems appear as special cases of a general theory covering the wider class of PMDs of linear systems. Among the topics covered are: real rational vector spaces and rational matrices, pole and zero structure of rational matrices at infinity, proper and omega stable rational fuctions and matrices. |

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### Contents

Polynomial Matrix Models of Linear Multivariable Systems | 54 |

Pole and Zero Structure of Rational Matrices at Infinity | 91 |

Dynamics of Polynomial Matrix Models | 153 |

Copyright | |

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### Common terms and phrases

biproper rational column degrees column proper column reduced common left divisor Consider Control coprime in Q Corollary defined Definition deg d(s denote Desoer Diophantine equations equivalence relation Euclidean division Example Exercise follows greatest common left holds true homogeneous matrix differential i.e. let IEEE Trans implies initial conditions internally proper invariant invariant polynomials Laplace transform left coprime Lemma let T(s linear systems matrix differential equation matrix pencil McMillan form minimal realization nn(s non-singular obtain oo of T(s PMD A(p pole-zero structure poles polynomial basis polynomial matrix Proof proper rational matrix Proposition Q S-MFDs Q-stable rankR rankR(s)T(s rational functions rational matrix T(s rational vector space reachable Remark right coprime right divisor Rosenbrock row column row proper satisfied Smith form Smith-McMillan form solution stabilizing compensator strict system equivalent strictly proper system equivalence system matrix TGL(s Theorem TL(s TR(s transfer function matrix unimodular matrix vector space zero structure