## Analysis and synthesis of time delay systemsThis book offers a comprehensive review of the modern theory of control systems described by functional-differential equations. The emphasis of the text is on methods and results that are applicable to analysis and synthesis of industrial control systems with time delays. Initial chapters contain examples of systems with delays and a presentation of typical control problems. Chapters also present basic results of the mathematical theory of functional-differential and discrete equations and cover identification of time-delay systems, stability theory, PID and Smith controllers, as well as the determination of stability regions, controller settings, and more. A review of controlability and observability results is presented, and optimal control is discussed in detail. |

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### Contents

Introduction | 1 |

Formulation of Control Problems | 24 |

Models of timedelay systems | 32 |

Copyright | |

9 other sections not shown

### Common terms and phrases

2kn+e absolutely continuous adjoint applied approximately controllable assume assumptions asymptotically stable Banach space boundary conditions bounded variation C0-semigroup characteristic function characteristic roots constant continuous function control systems defined Delfour denote derivative described determined differential equations equal to zero equilibrium point exists FDE system feedback finite function f given globally asymptotically stable Hence Hilbert space initial conditions input integrable interval Laplace transform Lemma Let us consider linear C0-semigroup linear regulator linear systems linear-quadratic problem lumped delay Lyapunov functional matrix Moreover necessary and sufficient nonlinear norm notation null-state controllable obtain operator optimal control optimal control problem optimal regulator output parameters performance functional polynomial proof quasipolynomial respect Riccati equation right-hand side satisfies Section selfadjoint semigroup Smith principle Smith-type regulation system stabilizability step method sufficient condition system equation Theorem theory trajectory transfer function unique solution variable variation-of-constants formula vector