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Dynamical Systems

  • Chapter
Stability of Dynamical Systems

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

Abstract

We give the definition of dynamical system and a classification of such systems: finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous and discontinuous systems; autonomous and non-autonomous systems; and composite systems. Classes of finite-dimensional dynamical systems that we address include systems determined by ordinary differential equations, ordinary differential inequalities, ordinary difference equations, and ordinary difference inequalities. General classes of infinite-dimensional dynamical systems that we address include systems determined by differential equations and inclusions defined on Banach spaces and systems determined by linear and nonlinear semigroups. Specific classes of infinite-dimensional dynamical systems that we address include systems determined by functional differential equations, Volterra integrodifferential equations, and certain classes of partial differential equations. For all cases, we present specific examples.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA

    Anthony N. Michel

  2. Department of Electrical and Computer Engineering, St. Cloud State University, St. Cloud, MN, USA

    Ling Hou

  3. Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL, USA

    Derong Liu

Authors
  1. Anthony N. Michel
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  2. Ling Hou
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  3. Derong Liu
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Michel, A.N., Hou, L., Liu, D. (2015). Dynamical Systems. In: Stability of Dynamical Systems. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15275-2_2

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