Input-to-state stability for PDEs. (2018)

• Record Type: Book
• Further Information: Note: Iasson Karafyllis, Miroslav Krstic.
• Authors: Karafyllis, Iasson; Krstić, Miroslav
• Contents: Intro; Preface; Contents; Abbreviations; Notation and Definitions; 1 Preview; 1.1 Introduction; 1.2 Topics and Tools in the Book; 1.3 Applications; 1.4 Background Material; 1.5 The ISS Property for Systems Containing PDEs; References; ISS for First-Order Hyperbolic PDEs; 2 Existence/Uniqueness Results for Hyperbolic PDEs; 2.1 Introduction; 2.2 Basic Existence/Uniqueness Results; 2.3 Examples; References; 3 ISS in Spatial Lp Norms for Hyperbolic PDEs; 3.1 Introduction; 3.2 ISS-Lyapunov Functionals; 3.3 ISS by Means of IDEs; References; ISS for Parabolic PDEs 4 Existence/Uniqueness Results for Parabolic PDEs4.1 Introduction; 4.2 Basic Existence/Uniqueness Results; 4.3 Nonlinear, Non-local Terms and Interconnections with ODEs; 4.4 Examples; 4.5 Boundary Inputs; References; 5 ISS in Spatial L2 and H1 Norms; 5.1 Introduction; 5.2 L2 Norm; 5.3 H1 Norm; 5.4 ISS Lyapunov Functionals; 5.5 Examples; 5.5.1 The Temperature of a Solid Bar; 5.5.2 Gain of R-A-D PDEs With Respect to Inlet Disturbances; References; 6 ISS in Spatial Lp Norms for Parabolic PDEs; 6.1 Introduction; 6.2 ISS-Lyapunov Functionals Under Discretization; 6.2.1 The Notion of the ISS-LFUD 6.2.2 Proof of Theorem 6.46.3 Deriving ISS Estimates; 6.3.1 ISS in the Sup-norm; 6.3.2 ISS in L1 Norm; 6.3.3 ISS in Lp Norms; 6.4 Applications; 6.4.1 Robustness of Backstepping with Respect to Actuator Errors; 6.4.2 ISS in Taylor-Couette Flow; References; Small-Gain Analysis; 7 Fading Memory Input-to-State Stability; 7.1 Introduction; 7.2 Two Basic Lemmas; References; 8 PDE-ODE Loops; 8.1 Introduction; 8.2 Hyperbolic PDE-ODE Loops; 8.3 Parabolic PDE-ODE Loops; 8.4 Applications; 8.4.1 A Chemical Reactor with a Cooling Jacket; 8.4.2 A Water Tank; 9 Hyperbolic PDE-PDE Loops; 9.1 Introduction 9.2 Existence/Uniqueness9.3 Small-Gain Analysis; 9.4 Comparison with Bastin-Coron Stability Conditions for Balance Laws; References; 10 Parabolic PDE-PDE Loops; 10.1 Introduction; 10.2 Existence/Uniqueness; 10.3 Small-Gain Analysis; Reference; 11 Parabolic-Hyperbolic PDE Loops; 11.1 Introduction; 11.2 Movement of Chemicals Underground; 11.3 Combination of Boundary and in-Domain Feedback Interconnection; References; Index
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource, illustrations
• Subjects: 515/.353; Engineering; Differential equations, Partial; Telecommunication; Systems theory; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Differential equations, Partial; Mathematics -- Differential Equations; Technology & Engineering -- Telecommunications; Science -- System Theory; Differential calculus & equations; Communications engineering / telecommunications; Cybernetics & systems theory; Technology & Engineering -- Automation; Automatic control engineering; Electronic books
• Languages: English
• ISBNs: 9783319910116; 3319910116
• Related ISBNs: 9783319910109; 3319910108
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed June 12, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.