## Algebraic Control Theory for Linear Multivariable Systems |

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### Contents

ALGEBRAIC CONTROL THEORY | 9 |

Introduction | 18 |

Introduction | 150 |

Copyright | |

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### Common terms and phrases

A-generalized polynomial matrix A-stable algebraic bijective chapter class H closed loop system column degrees column proper complex plane controllability indices Corollary corresponding decoupling zeros defined definition deg det T(q described determine discrete time systems disturbance equal equations equivalence relation euclidean domain feedback controller follows from theorem form in q fractional representation ft-stable Furthermore given gives input Insert invariant factors invariant under equivalence Laurent polynomial matrix left A-structure matrix left divisor lemma linear map linearly independent columns linearly independent rows monic polynomial multiplication nomial nonsingular nonzero nullspace Observe obtained output poles polynomial basis principal ideal domain problem Proof rational functions relatively left prime right A-invertible right A-structure matrix Rosenbrock 1970 satisfying servo shown solution stable and causal standard polynomial form subspace Suppose system in figure theorem 2.6 tion transfer func transfer function unimodular matrix unimodular polynomial matrix unique unstable region variables vector vector space Wonham