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Introductory Concepts

Domitilla Del Vecchio and Richard M. Murray

in Biomolecular Feedback Systems

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161532
eISBN:
9781400850501
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161532.003.0001
Subject:
Biology, Biochemistry / Molecular Biology

This chapter provides a brief introduction to concepts from systems biology; tools from differential equations and control theory; and approaches to the modeling, analysis, and design of biomolecular ... More


Analysis of Dynamic Behavior

Domitilla Del Vecchio and Richard M. Murray

in Biomolecular Feedback Systems

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161532
eISBN:
9781400850501
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161532.003.0003
Subject:
Biology, Biochemistry / Molecular Biology

This chapter turns to some of the tools from dynamical systems and feedback control theory that will be used in the rest of the text to analyze and design biological circuits. It first models the ... More


Matrix Completions, Moments, and Sums of Hermitian Squares

Mihály Bakonyi and Hugo J. Woerdeman

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691128894
eISBN:
9781400840595
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691128894.001.0001
Subject:
Mathematics, Computational Mathematics / Optimization

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly ... More


System-level Properties as Numerical Invariants

Pierre-Loïc Garoche

in Formal Verification of Control System Software

Published in print:
2019
Published Online:
January 2020
ISBN:
9780691181301
eISBN:
9780691189581
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691181301.003.0007
Subject:
Mathematics, Applied Mathematics

This chapter summarizes an attempt to express classical notions of control theory such as stability or robustness using the previously presented invariant-based tools. All numerical tools presented ... More


Definitions—Background

Pierre-Loïc Garoche

in Formal Verification of Control System Software

Published in print:
2019
Published Online:
January 2020
ISBN:
9780691181301
eISBN:
9780691189581
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691181301.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter presents the formalisms describing discrete dynamical systems and gives an overview on the convex optimization tools and methods used to compute the analyses. A dynamical system is a ... More


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