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Stability of nonlinear systems containing time delays and/or sampling operations

Stability of nonlinear systems containing time delays and/or sampling operations and =Jc - di3 6 1- E i Vi = ni Jc -6 (4‘4) Substitution of Equations (2A), (3A), and (4A) into Equation ( 1 A ) yields 3 - FA - 8(1 - 4 ) (5A) 2 (Pd-fpc) 1 - Bi 2- di The definition of the mean diameter d, of a mixture assumes that the active forces are the same. Comparison of Equations ( 5 A ) and (7A) yields the definition of the mean diameter d,, as expressed in Equation ( 7 ) . Manuscript received January 16, 1970; revision recelved June 12, 1970; paper accepted June 18, 1970. The friction forces on the total surface (XAi), exposed by Stability of Nonlinear Systems Containing Time Delays and/or Sampling Operations DALE E. SEBORG and ERNEST F. JOHNSON Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08540 In recent years the stability of nonlinear systems has been a topic of considerable interest. Relatively little attention, however, has been directed toward nonlinear timedelay systems, that is, systems whose dynamic behavior is described by a set of differential-difference equations. Although the fundamental stability theorems of Liapunov’s Correspondence concerning this article should be addressed to Prof. I>. E. Seborg http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aiche Journal Wiley

Stability of nonlinear systems containing time delays and/or sampling operations

Seborg, Dale E.; Johnson, Ernest F.
Aiche Journal , Volume 17 (4) – Jul 1, 1971
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Publisher
Wiley
Copyright
Copyright © 1971 American Institute of Chemical Engineers
ISSN
0001-1541
eISSN
1547-5905
DOI
10.1002/aic.690170419
Publisher site
See Article on Publisher Site

Abstract

and =Jc - di3 6 1- E i Vi = ni Jc -6 (4‘4) Substitution of Equations (2A), (3A), and (4A) into Equation ( 1 A ) yields 3 - FA - 8(1 - 4 ) (5A) 2 (Pd-fpc) 1 - Bi 2- di The definition of the mean diameter d, of a mixture assumes that the active forces are the same. Comparison of Equations ( 5 A ) and (7A) yields the definition of the mean diameter d,, as expressed in Equation ( 7 ) . Manuscript received January 16, 1970; revision recelved June 12, 1970; paper accepted June 18, 1970. The friction forces on the total surface (XAi), exposed by Stability of Nonlinear Systems Containing Time Delays and/or Sampling Operations DALE E. SEBORG and ERNEST F. JOHNSON Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08540 In recent years the stability of nonlinear systems has been a topic of considerable interest. Relatively little attention, however, has been directed toward nonlinear timedelay systems, that is, systems whose dynamic behavior is described by a set of differential-difference equations. Although the fundamental stability theorems of Liapunov’s Correspondence concerning this article should be addressed to Prof. I>. E. Seborg

Journal

Aiche Journal – Wiley

Published: Jul 1, 1971

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