Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

93Dxx Stability and stabilization

This subtopic introduces the core ideas in stability and stabilization, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.) in control theory

Overview

This specific topic studies lyapunov and other classical stabilities (lagrange, poisson, $l^p, l^p$, etc.) in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.) in control theory

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Lyapunov and other classical stabilities (Lagrange, Poisson, L^p, l^p, etc.) in control theory. Available via Amazon search. — Amazon · Bookshop.org

93D09 Robust stability in control theory

Overview

This specific topic studies robust stability in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Robust stability in control theory

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Robust stability in control theory. Available via Amazon search. — Amazon · Bookshop.org

93D10 Popov-type stability of feedback systems

Overview

This specific topic studies popov-type stability of feedback systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Popov-type stability of feedback systems

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Popov-type stability of feedback systems. Available via Amazon search. — Amazon · Bookshop.org

93D15 Stabilization of systems by feedback

Overview

This specific topic studies stabilization of systems by feedback within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Stabilization of systems by feedback

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Stabilization of systems by feedback. Available via Amazon search. — Amazon · Bookshop.org

93D20 Asymptotic stability in control theory

Overview

This specific topic studies asymptotic stability in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Asymptotic stability in control theory

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Asymptotic stability in control theory. Available via Amazon search. — Amazon · Bookshop.org

93D21 Adaptive or robust stabilization

Overview

This specific topic studies adaptive or robust stabilization within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Adaptive or robust stabilization

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Adaptive or robust stabilization. Available via Amazon search. — Amazon · Bookshop.org

93D23 Exponential stability

Overview

This specific topic studies exponential stability within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia: Exponential stability

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Exponential stability. Available via Amazon search. — Amazon · Bookshop.org

93D30 Lyapunov and storage functions

Overview

This specific topic studies lyapunov and storage functions within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Lyapunov and storage functions

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Lyapunov and storage functions. Available via Amazon search. — Amazon · Bookshop.org

93D40 Finite-time stability

Overview

This specific topic studies finite-time stability within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Finite-time stability

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Finite-time stability. Available via Amazon search. — Amazon · Bookshop.org

93D50 Strongly asymptotically stable nonlinear systems in control theory

Overview

This specific topic studies strongly asymptotically stable nonlinear systems in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Strongly asymptotically stable nonlinear systems in control theory

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Strongly asymptotically stable nonlinear systems in control theory. Available via Amazon search. — Amazon · Bookshop.org