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                "title": "Robust Performance",
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                        "*": "{{Chapter\n|Chapter number=13\n|Short name=robperf\n|Previous chapter=Frequency Domain Design\n|Next chapter=Fundamental Limits\n|First edition URL=https://www.cds.caltech.edu/~murray/amwiki/index.php?title=Robust_Performance#Frequently_Asked_Questions\n|Chapter summary=This chapter focuses on the analysis of robustness of feedback systems, a vast topic for which we provide only an introduction to some of the key concepts. We consider the stability and performance of systems whose process dynamics are uncertain. We make use of generalizations of Nyquist\u2019s stability criterion as a mechanism to characterize robust stability and performance. To do this we develop ways to describe uncertainty, both in the form of parameter variations and in the form of neglected dynamics. We also briefly mention some methods for designing controllers to achieve robust performance.\n|Chapter contents=# Modeling Uncertainty\n#* Parametric Uncertainty\n#* Unmodeled Dynamics\n#* When Are Two Systems Similar?\n#* The Vinnicombe Metric\n# Stability in the Presence of Uncertainty\n#* Robust Stability Using Nyquist's Criterion\n#* Youla Parameterization\n# Performance in the Presence of Uncertainty\n#* Disturbance Attenuation\n#* Response to Reference Signals\n# Design for Robust Performance\n#* Quantitative Feedback Theory\n#* Linear Quadratic Control\n#* $H\\relax \\p@index \\infty $ Control\n#* The Generalized Stability Margin\n#* Disturbance Weighting\n#* Limits of Robust Design\n# Further Reading\n:: Exercises\n}}\n{{Chapter footer}}"
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            "113": {
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                "title": "Software",
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                        "*": "{{righttoc}}\nA wealth of software is available for analysis, design and implementation of feedback systems.\nThis page contains information on ''open source'' software that is being developed to support the analysis and design techniques described in ''Feedback Systems''.\n\n=== Python Control Systems Library (python-control) ===\n\nA library of functions for analysis and design of control systems is being developed for use in the Python programming language.  The python-control package is an open source project that is intended to implement the standard control system functions.  More information is available at:\n\n* http://python-control.org - python-control wiki page (includes download instructions and examples)\n\nThe current release of this software includes the ability to generate most of the figures in the book.  Links to individual [[:Category:Figures|figures]] and [[:Category:Examples|examples]] are available on chapter pages.  To run some of the code used to generate these figures, you may need additional files available here:\n\n* https://github.com/murrayrm/fbs2e-python\n\n=== Sparrow Real-Time Control Libraries ===\n\nThe [https://github.com/murrayrm/sparrow Sparrow project] at Caltech is a collection of open source C/C++ libraries for implementing real-time controllers on Linux-based data acquisition & control systems. Two low-level libraries that allow implementation of the controllers described in the text are available:\n* [https://github.com/murrayrm/sparrow Sparrow] - a real-time library that supports control loops, device interfaces, real-time displays\n* Falcon - a library for implementing standard control techniques such as state space compensators and Kalman filters.  (The linux version of the falcon library will be released in the near future.)\nIn addition, some more advanced libraries are being developed for use in networked control environments:\n* Skynet - a messaging library for communication between processing using the Spread communications protocol\n* [https://github.com/murrayrm/ntg NTG] - nonlinear trajectory generation library, including receding horizon control (RHC)\n\n=== Other Software Packages ===\n\n==== Analysis and Design Tools ====\n\n* [https://github.com/JuliaControl Julia] - Control Systems Design in Julia\n* [http://aer.ual.es/ilm/ Interactive Learning Modules Project] - interactive tools for PID control\n* [http://www.gnu.org/software/octave/ Octave] (GNU) - open source MATLAB replacement\n* [http://www.scilab.org/ Scilab] (INRIA) - open source MATLAB replacement\n\n==== Control Implementation Libraries ====\n\n* [https://www.comedi.org Comedi] - Linux control and measurement interface; device drivers for data acquisition cards\n* [https://www.nist.gov/el/intelligent-systems-division-73500/networked-control-systems-group/real-time-control-systems Real-Time Control Systems Library] (NIST)\n* [http://ros.org ROS] - open-source, meta-operating system for robotics applications"
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