## 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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**theorem**This small - gain result complements Lemma A.1 in [ 11 ] and Lemma 3.4 in [ 30 ] .**Theorem**1. Let μa and μ be input measures . Suppose given a KL - function ß , a number ro≥0 , a K - function y for which y ( r ) < r if r > ro ...Page 222

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**Theorem**1. For ease of reference , we present the small - gain results in [ 11 ] and [ 33 ] and indicate how they follow from**Theorem**1 . 4.5.1 . IOS - finite dimensional state space representation We begin by showing how**Theorem**1 can ...Page 524

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**Theorem**is a direct consequence of Definition 2 , Lemma 2 and the fact that the denominator of p ( G ( s ) ) is a Hurwitz polynomial . Lemma 2 and**Theorem**3 establish simple solutions to the first problem . Corollary 4. If N ( s ) / D ...### Contents

Contents | 1 |

Vol 339 No 2 MARCH 2002 | 129 |

PERGAMON ISSN 00160032 | 248 |

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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