## Linear System Theory"Linear System Theory, Second Edition," outlines the basic theory of linear systems in a unified, accessible, and careful manner, with parallel, independent treatment of continuous-time and discrete-time linear systems. |

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### Contents

STATE EQUATION REPRESENTATION | 20 |

STATE EQUATION SOLUTION | 36 |

TWO IMPORTANT CASES | 66 |

Copyright | |

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### Common terms and phrases

Automatic Control Ax(t bounded-output stable Bu(t Chapter characteristic polynomial closed-loop state equation coefficient matrices compute controllability and observability controllability subspace controlled invariant subspace coprime corresponding Cx(t defined Definition diagonal differential equation eigenvalues elementary row operations entries equation x(t Example Exercise exists feedback gain geometric Hankel matrix IEEE Transactions implies impulse response input signal integrator invariant subspace contained invertible Laplace transform left polynomial fraction Lemma linear combination linear state equation linear systems linearly independent m x n matrix exponential maximal controlled invariant minimal realization n x 1 vector n x n matrix nonzero norm notation Note output feedback polynomial fraction description polynomial matrix proof of Theorem properties right polynomial fraction satisfies scalar single-input solution Theorem Suppose time-invariant linear time-varying time-varying systems tion Transactions on Automatic transition matrix uniform exponential stability uniformly bounded-input uniformly exponentially stable unimodular unimodular matrix variable change zero-state response