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Titlebook: Input-to-State Stability for PDEs; Iasson Karafyllis,Miroslav Krstic Book 2019 Springer Nature Switzerland AG 2019 Input-to-State Stabilit

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Parabolic–Hyperbolic PDE Loopsof a parabolic PDE with a first-order hyperbolic PDE by means of a combination of boundary and in-domain terms. The interconnection is effected by linear, non-local terms. For both cases, results for existence/uniqueness of solutions as well as sufficient conditions for ISS or exponential stability in the spatial sup-norm are provided.
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0178-5354 PDEs with non-local terms.Equips the reader for a large numbThis book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. .In addition t
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ISS in Spatial , Norms for Parabolic PDEsis explained in detail. The obtained ISS estimates are employed to show ISS for Taylor–Couette flow and to show that recently proposed backstepping boundary feedback controllers for parabolic PDEs guarantee robustness with respect to control actuator errors.
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Parabolic PDE-PDE Loopsctions. Sufficient small-gain conditions for ISS in the spatial . norm and the spatial . norm are provided. The chapter also includes the development of existence/uniqueness for initial-boundary value problems of systems of parabolic PDEs with non-local terms.
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