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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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