Biomolecular Feedback Systems

Princeton University Press
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This book provides an accessible introduction to the principles and tools for modeling, analyzing, and synthesizing biomolecular systems. It begins with modeling tools such as reaction-rate equations, reduced-order models, stochastic models, and specific models of important core processes. It then describes in detail the control and dynamical systems tools used to analyze these models. These include tools for analyzing stability of equilibria, limit cycles, robustness, and parameter uncertainty. Modeling and analysis techniques are then applied to design examples from both natural systems and synthetic biomolecular circuits. In addition, this comprehensive book addresses the problem of modular composition of synthetic circuits, the tools for analyzing the extent of modularity, and the design techniques for ensuring modular behavior. It also looks at design trade-offs, focusing on perturbations due to noise and competition for shared cellular resources.

Featuring numerous exercises and illustrations throughout, Biomolecular Feedback Systems is the ideal textbook for advanced undergraduates and graduate students. For researchers, it can also serve as a self-contained reference on the feedback control techniques that can be applied to biomolecular systems.

  • Provides a user-friendly introduction to essential concepts, tools, and applications
  • Covers the most commonly used modeling methods
  • Addresses the modular design problem for biomolecular systems
  • Uses design examples from both natural systems and synthetic circuits
  • Solutions manual (available only to professors at
  • An online illustration package is available to professors at
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About the author

Domitilla Del Vecchio is associate professor of mechanical engineering at the Massachusetts Institute of Technology. Richard M. Murray is professor of control and dynamical systems and bioengineering at the California Institute of Technology. His books include Feedback Systems: An Introduction for Scientists and Engineers (Princeton).
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Additional Information

Princeton University Press
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Published on
Oct 26, 2014
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Mathematics / Applied
Mathematics / Differential Equations / General
Mathematics / Study & Teaching
Science / Life Sciences / Biology
Science / Life Sciences / Molecular Biology
Technology & Engineering / Biomedical
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Content Protection
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Eligible for Family Library

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This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems.

Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences.

Covers the mathematics needed to model, analyze, and design feedback systems Serves as an introductory textbook for students and a self-contained resource for researchers Includes exercises at the end of every chapter Features an electronic solutions manual Offers techniques applicable across a range of disciplines
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