Stability in feedback systems with tapered and other special input spaces

Serakos, Demetrios

doi:10.1109/9.151121

Cited by 6 publications

(8 citation statements)

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“…This is Equation . The operator maps F to G. Equation (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) gives the auxiliary map to compute G A # = B # 2 Y a . At the top of Figure 2, the generalized adjoint gives F a B # = B # F 2 U a .…”

Section: Discussionmentioning

confidence: 99%

“…The lower portion of Figure 2 depicts the situation. Four equations give the essentials: Equations (6-5), (6-21), (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22), and (6-23). Starting with u 2 U , following Figure 2, the operator maps U onto U # .…”

Section: Discussionmentioning

confidence: 99%

“…Roughly speaking, …tted families work like L p norms on time functions with the additional feature where a time weighting can be incorporated so the distant past of an input or output time function may be de-emphasized. 1 This feature is not as important in this report as it is in [11] or [13]. The notation ku s;t k s;t indicates the norm; e.g., a weighted L p norm, of the input u over the interval of time (s; t].…”

Section: Introductionmentioning

confidence: 99%

“…Let B # = G(A # ) and A # F a (B # ) as in (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23). Then D(F a (B # )) = A # so de…ned is bounded and continuous.…”

Section: Proof: Boundedness: Considermentioning

confidence: 99%

“…An alternative to and (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) are A # (u)(t) = (ut u # t ) (t) and G(A # )(y)(t) = (yt e Ft(u # t )) (t) where : Ut ! < is the delta function, that is (ut) = 1 if ut is zero and = 0 else.…”

Section: Proof: Memoryless: Considermentioning

confidence: 99%

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Generalized Adjoint Systems

Serakos¹

2012

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTES ABSTRACTA generalized adjoint system is defined. Using a given input-output system, the generalized adjoint system is patterned similarly to adjoints of bounded linear transformations. Elementary properties of the generalized adjoint system are derived. For a space of input-output systems, a generalized adjoint map from this space of systems to the space of generalized adjoints is defined. Properties of the generalized adjoint map are derived. It is shown that the inverse of an inputoutput system may be represented in terms of the generalized adjoint. The use of the generalized adjoint system to determine noise and disturbance bounds for an input-output system is shown. This is similar to the method of adjoints in linear systems theory. An example is presented. * This report defines and develops the generalized adjoint of an input-output system. The generalized adjoint of a system may be used to represent the inverse of a system, which may be used in systems analysis. Furthermore, the generalized adjoint condenses system behavior in a way that facilitates analysis of the effect of noise and disturbance on a system. SUBJECT TERMS

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Let B # = G(A # ) and A # F a (B # ) as in (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23). Then D(F a (B # )) = A # so de…ned is bounded and continuous.…”

Section: Proof: Boundedness: Considermentioning

confidence: 99%

Section: Proof: Memoryless: Considermentioning

confidence: 99%

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Generalized Adjoint Systems

Serakos¹

2012

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Introduction

Serakos¹

2014

SpringerBriefs in Optimization

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Generalized Adjoint Systems

Serakos¹

2015

SpringerBriefs in Optimization

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SpringerBriefs in Optimization showcases algorithmic and theoretical techniques, case studies, and applications within the broad-based field of optimization. Manuscripts related to the ever-growing applications of optimization in applied mathematics, engineering, medicine, economics, and other applied sciences are encouraged.More information about this series at of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. ForewordThis book is the result of a theoretical development and examination of the generalized adjoint concept and the conditions under which systems analysis using adjoints is valid. The results developed in this book are useful aids for the analysis and modeling of physical systems, including the development of guidance and control algorithms, and in developing simulations. 1 This book defines and develops the generalized adjoint of an input-output system. The generalized adjoint of a system may be used to represent the inverse of a system, which may be used in systems analysis. Furthermore, the generalized adjoint condenses system behavior in a way that facilitates analysis of the effect of noise and disturbance on a system.

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Stability in feedback systems with tapered and other special input spaces

Cited by 6 publications

References 4 publications

Generalized Adjoint Systems

Generalized Adjoint Systems

Introduction

Generalized Adjoint Systems

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