Nonsmooth Lyapunov analysis in finite and infinite dimensions. (2020)

• Record Type: Book
• Further Information: Note: Yury Orlov.
• Other Names: Orlov, I︠U︡. V (I︠U︡riĭ Vladimirovich)
• Contents: Intro -- Foreword -- Preface -- Contents -- Abbreviations -- Part I Introduction -- 1 Benchmark Models -- 1.1 Variable Structure Systems -- 1.1.1 First- and Higher-Order Sliding Modes -- 1.1.2 Chattering Phenomenon and Discrete-Time Sliding Modes -- 1.1.3 Infinite-Dimensional Sliding Modes -- 1.2 Dynamics Under Unilateral Constraints -- 1.2.1 Zhuravlev-Ivanov Transformation -- 1.2.2 Bouncing Ball: State Resets and Zeno Behavior -- 1.2.3 Constrained Van der Pol Oscillator: Limit Cycles and Hopf Bifurcation -- 1.3 Concluding Remarks -- References -- 2 Mathematical Background 2.1 Comparison Principle and Barbalat's Lemma -- 2.2 Discontinuous and Multi-valued Vector Fields -- 2.2.1 Filippov Solutions -- 2.2.2 Equivalent Control Method and Other Solution Concepts -- 2.2.3 Ambiguous Sliding Modes -- 2.2.4 Uniqueness of Sliding Modes in Affine Systems -- 2.2.5 Regularization of Discontinuous Systems in Hilbert Space -- 2.3 Complementarity Formulation of Constrained Lagrange Dynamics -- 2.3.1 Implicit Euler Integration of Sliding Modes -- 2.4 Hopf Bifurcation of Discontinuous Limit Cycles: Case Study -- 2.4.1 Constrained Van der Pol Oscillator 2.4.2 Existence of a Constrained Limit Cycle -- 2.4.3 Numerical Analysis of Phenomenological Behaviors -- 2.4.4 Hopf Bifurcation Analysis via Poincaré Method -- 2.4.5 Constrained Van der Pol Oscillator with Manipulated Parameters -- 2.5 Concluding Remarks -- References -- 3 Mathematical Tools of Dynamic Systems in Hilbert Spaces -- 3.1 Sobolev Spaces and Instrumental Inequalities -- 3.2 Linear Partial Differential Equations -- 3.2.1 Linear Differential Operators -- 3.2.2 Parabolic, Elliptic, and Hyperbolic Operators -- 3.2.3 Green Function and Mild Solutions -- 3.2.4 Weak Solutions 3.3 Sturm-Liouville Operators and Their Properties -- 3.3.1 Eigenvalue Estimates -- 3.3.2 Uniform Boundedness of the Eigenfunctions -- 3.4 Separation of Variables -- 3.4.1 Parabolic Case Study -- 3.4.2 Hyperbolic Case Study -- 3.5 Nonlinear First-Order Partial Differential Equations -- 3.5.1 Viscosity Solutions of First-Order PDEs -- 3.5.2 Discontinuous Strict Hamilton-Jacobi Inequality and Its Proximal Solutions -- 3.6 Stability in Euclidean and Hilbert Spaces -- 3.6.1 Abstract Dynamic Systems and Relevant Stability Concepts 3.6.2 Robust Stability of Uncertain Dynamic Systems: Basic Definitions -- 3.6.3 Sliding Mode Dynamics in Hilbert Space -- 3.6.4 Hilbert Space-Valued Dynamics with Delay -- 3.6.5 Homogeneous Differential Inclusions and Their Finite Time Stability -- 3.7 Concluding Remarks -- References -- Part II Construction of Nonsmooth Lyapunov Functions -- 4 Modern Lyapunov Tools -- 4.1 Strict Lyapunov Functionals -- 4.1.1 Multiple Lyapunov Functionals -- 4.1.2 Semi-global Lyapunov Functionals -- 4.1.3 Finite Time Stable Lyapunov Functionals -- 4.1.4 Homogeneous Lyapunov Functions
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (351 pages)
• Subjects: 515/.392; Lyapunov functions; Lyapunov stability; Lyapunov functions; Lyapunov stability; Electronic books
• Languages: English
• ISBNs: 9783030376253; 3030376257
• Related ISBNs: 9783030376246
• Notes: Note: Includes bibliographical references.; Note: Print version record.
• 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.