## Mathematical Control Theory: Deterministic Finite Dimensional SystemsMathematics is playing an ever more important role in the physical and biologi cal sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein force the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematics Sci ences (AMS) series, which will focus on advanced textbooks and research-level monographs. v Preface to the Second Edition The most significant differences between this edition and the first are as follows: • Additional chapters and sections have been written, dealing with: nonlinear controllability via Lie-algebraic methods, variational and numerical approaches to nonlinear control, including a brief introduction to the Calculus of Variations and the Minimum Principle, - time-optimal control of linear systems, feedback linearization (single-input case), nonlinear optimal feedback, controllability of recurrent nets, and controllability of linear systems with bounded controls. |

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### Contents

Introduction | 1 |

Systems | 25 |

Reachability and Controllability | 81 |

Nonlinear Controllability | 141 |

Feedback and Stabilization | 183 |

Outputs | 261 |

Observers and Dynamic Feedback | 315 |

Optimality Value Function | 347 |

Optimality Multipliers | 397 |

Optimality MinimumTime for Linear Systems | 423 |

Linear Algebra | 447 |

Differenctials | 461 |

Ordinary Differential Equations | 467 |

### Other editions - View all

Mathematical Control Theory: Deterministic Finite Dimensional Systems Eduardo D. Sontag Limited preview - 2013 |

Mathematical Control Theory: Deterministic Finite Dimensional Systems Eduardo D Sontag Limited preview - 2012 |

### Common terms and phrases

algebraic analytic applied arbitrary Assume asymptotically behavior bounded called columns compact complete compute conclude condition consider constant continuous continuous-time system convergent Corollary corresponding cost defined definition denote derivative desired differential equation discrete-time discussed dynamic eigenvalues elements equal equivalent establish example Exercise exists fact feedback final finite fixed follows function given gives globally holds implies independent initial input instance integrable interval Lemma linear systems locally matrix means measurable minimal neighborhood nonlinear norm Note observable obtained open subset operator optimal control original output pair particular Pick polynomial positive possible problem Proof Proposition prove provides rank reachable realization references Remark respect restriction satisfies sequence smooth solution solve space stability Suppose Theorem theory time-invariant trajectory unique vector fields write zero

### Popular passages

Page 505 - B. Jakubczyk and W. Respondek. 'On Linearization of Control Systems.' Bull. Acad. Pol. Sci. . Ser. Sci. Math. Astronom. Phys. 2fi. (1980). [35] R. Su, 'On the Linear Equivalence of Nonlinear Systems.