Elements of Nonsmooth Analysis

  • Yury V. Orlov
  • Luis T. Aguilar
Part of the Systems & Control: Foundations & Applications book series (SCFA)


A differential construct that applies to nonsmooth functions is useful in general. The proximal supergradient admits a very complete calculus for upper semicontinuous functions and perfectly suits the nonsmooth \(\mathcal{L}_{2}\)-gain analysis to be developed in this chapter.


Nonsmooth analysis Proximal sub(super)-gradient First-order PDE Viscosity solution Hamilton–Jacobi inequality 


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Copyright information

© Springer Science+Business Media, New York 2014

Authors and Affiliations

  • Yury V. Orlov
    • 1
  • Luis T. Aguilar
    • 2
  1. 1.Electronics and TelecommunicationCICESE Research CenterEnsenadaMexico
  2. 2.Centro de Investigación y Desarrollo de Tecnología DigitalInstituto Politécnico NacionalTijuanaMexico

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