## Journal of the Franklin Institute, Volume 339Pergamon Press, 2002 Vols. 1-69 include more or less complete patent reports of the U. S. Patent Office for years 1825-1859. cf. Index to v. 1-120 of the Journal, p. [415] |

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**denote**the subset of nonnegative elements of 7. By notational convention , in what follows , all intervals are ...**denote**the unique maximal solution of the initial value problem x = f ( x , u ) , x ( 0 ) = ¿ , defined on a maximal ...Page 377

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**denote**an estimate before ( − ) or after ( + ) an update . If a process is sampled every T seconds , the discrete sequence so generated is written { y [ k ] } , where the index**denotes**sample number rather than time . Conditional ...Page 467

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**Denote**by x4 and xs the temperatures of water in T2 and T3 which are assumed to be stirred . t and t '**denote**the respective temperatures of water in 71 and the ambient which are assumed to be constant . Now set u the power of the ...### Contents

Contents | 1 |

Vol 339 No 2 MARCH 2002 | 129 |

PERGAMON ISSN 00160032 | 248 |

Copyright | |

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2002 The Franklin adaptive algorithm analysis angiogenesis applied approach Benjamin Franklin Medal Chebyshev Chebyshev polynomials chirp closed-loop computation consider constraints corresponding coset defined denote detection domain dynamic systems Elsevier Science Ltd encoding energy equation estimation example fault fault-tolerant feedback finite flywheel Franklin Institute Franklin Institute 339 Franklin Institute www.elsevier.com/locate/jfranklin frequency response frequency response functions gain given group machine homomorphism IEEE IEEE Trans implementation input k₁ mapping Mathematics matrix method NARMAX model noise nomograph nonlinear systems observer obtained optimal control optimal control problem output packet paleomagnetic paper parameters performance Petri net phase error PID controller polynomials proposed Published by Elsevier quadratic redundant residual ScienceDirect Section selectivity semiautomata semigroup shown in Fig signal processing simulation solution solve SPRO stability T₁ TDTL Theorem trajectories transfer function transform transitional filter University v₁ variables vector Widrow zero