LMI-Based \(\mathcal{H}_{\infty }\)-Boundary Control of Nonsmooth Parabolic and Hyperbolic Systems

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


This chapter develops, in side-by-side fashion, exponential stability analysis and \(\mathcal{L}_{2}\)-gain analysis via the Lyapunov method for scalar uncertain distributed parameter systems, governed by nonsmooth partial differential equations of the parabolic and hyperbolic types. The nonsmooth uncertainties are admitted to be time-, space-, and state-dependent, with a priori known upper and lower bounds. Sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities for both systems. These conditions are then utilized to synthesize \(\mathcal{H}_{\infty }\)-static output-feedback boundary controllers of the systems in question. Numerical examples illustrate the efficacy of the method.


Semilinear parabolic system Semilinear hyperbolic system Boundary control Boundary sensing Disturbance attenuation 


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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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