## Algebra, with Applications to Physics and Systems Theory: Algebraic topics in systems theory |

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### Contents

A1 | |

THE CONSTITUATIVE RELATIONS FOR ELECTRIC NETWORKS | |

THE GENERAL FORM OF LINEAR TIME INVARIANT CIRCUIT | |

Copyright | |

3 other sections not shown

### Common terms and phrases

algebraic basis branch Brockett called canonical form Cauchy problem Chapter circuit theory complex numbers Consider constituative relations curve defined Definition denote Desoer DGCV differen dimensional vector spaces dual vector elements Euler-Lagrange equations exp(tA extremal field finite dimensional vector flow following condition following form formulas free vector space function geometric GL(V graph Hamilton equations Hamilton-Jacobi equation Hamilton-Jacobi theory Hamiltonian Hence homomorphism inductor infinitesimal Introduction Lagrangian subspace Laplace transform Lie systems linear fractional transformation linear maps linear ordinary differential linear subspace manifolds mathematical matrix Riccatti equation non-zero notation one-one operator optimal control theory orbit ordinary differential equations polynomial projection map Proof properties prove quadratic real numbers real variable real vector space Remark rm(V scalar Section solutions of 6.7 stability subgroup Suppose systems theory takes the following Theorem 3.1 tial equation tion transformation group variational problem vector space voltage