## Introduction to dynamic systems: theory, models, and applicationsIntegrates the traditional approach to differential equations with the modern systems and control theoretic approach to dynamic systems, emphasizing theoretical principles and classic models in a wide variety of areas. Provides a particularly comprehensive theoretical development that includes chapters on positive dynamic systems and optimal control theory. Contains numerous problems. |

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### Contents

INTRODUCTION | 1 |

DIFFERENCE AND DIFFERENTIAL EQUATIONS | 14 |

LINEAR ALGEBRA | 55 |

Copyright | |

11 other sections not shown

### Common terms and phrases

algebra analysis applied arbitrary assume asymptotically stable Ax(k basis behavior canonical forms chapter characteristic equation characteristic polynomial closed class coefficients column completely controllable components Consider constant continuous-time systems converges corresponding defined definition denote derived determined diagonal difference equation differential equations discrete-time discrete-time system dominant eigenvalue dynamic system eigenvalue elements equal equilibrium point example expressed feedback finite follows Frobenius-Perron Gambler's Ruin geneotype geometric sequence given growth homogeneous equation initial conditions input left eigenvector Liapunov function linear combination linear systems linearly independent Markov chain mathematical multiple nonhomogeneous nonnegative nonzero nth-order nxn matrix optimal control optimal control problem original system output parameters population positive systems possible probability probability vector represents result roots satisfy Sect Show simple solution specific state-transition matrix structure Suppose system equation system matrix system x(k Theorem theory tion trajectory transfer function transform variables vector yields z-transform zero