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Path Integrals and Stability

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Mathematical Control Theory

Abstract

A path integral associated with a dynamical system is an integral of a memoryless function of the system variables which, when integrated along trajectories of the system, depends only on the value of the trajectory and its derivatives at the endpoints of the integration interval. In this chapter we study path independence for linear systems and integrals of quadratic differential forms. These notions and the results are subsequently applied to stability questions. This leads to Lyapunov stability theory for autonomous systems described by high-order differential equations, and to more general stability concepts for systems in interaction with their environment. The latter stability issues are intimately related to the theory of dissipative systems.

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Authors
  1. J. C. Willems
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Editor information

Editors and Affiliations

  1. College of Engineering, Boston University, Boston, MA, 02215-2407, USA

    J. Baillieul

  2. Mathematics Institute, University of Groningen, 9700 AV, Groningen, The Netherlands

    J. C. Willems

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© 1999 Springer Science+Business Media New York

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Willems, J.C. (1999). Path Integrals and Stability. In: Baillieul, J., Willems, J.C. (eds) Mathematical Control Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1416-8_1

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  • DOI: https://doi.org/10.1007/978-1-4612-1416-8_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7136-9

  • Online ISBN: 978-1-4612-1416-8

  • eBook Packages: Springer Book Archive

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