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Stability --- Differential equations, Nonlinear --- Nonlinear theories --- Congresses --- Congresses. --- Stability - Congresses --- Differential equations, Nonlinear - Congresses --- Nonlinear theories - Congresses

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Ordinary differential equations --- Differential equations --- Integral equations --- Stability --- Congresses --- Differential equations - Congresses --- Integral equations - Congresses --- Stability - Congresses

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Stochastic processes --- Stochastic systems --- Stochastische systemen --- Systemes stochastiques --- Stability --- Stabilité --- Systèmes stochastiques --- Congresses --- Congrès --- Congresses. --- 51 --- -Stability --- -Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Systems, Stochastic --- System analysis --- Mathematics --- -Mathematics --- 51 Mathematics --- -51 Mathematics --- Stabilité --- Systèmes stochastiques --- Congrès --- Stochastic systems - Congresses. --- Stability - Congresses.

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This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session "Stability and Bifurcation Problems for Non-Autonomous Differential Equations," held in Cetraro, Italy, June 19-25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree-theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability/bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional-differential equations. The volume will be of interest to all researchers working in these and related fields.

Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations, Nonlinear --- Stability --- Bifurcation theory --- Mathematics. --- Difference equations. --- Functional equations. --- Dynamics. --- Ergodic theory. --- Differential equations. --- Ordinary Differential Equations. --- Difference and Functional Equations. --- Dynamical Systems and Ergodic Theory. --- 517.91 Differential equations --- Differential equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Equations, Functional --- Functional analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Math --- Science --- Differential Equations. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Differential equations, Nonlinear - Congresses --- Stability - Congresses --- Bifurcation theory - Congresses

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Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of stability and feedback stabilization methods, which enables the reader to learn and understand major techniques used in mathematical control theory. In particular: • the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization; • a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems; • approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and • new tools for stability analysis and control design of a wide class of nonlinear systems are introduced. The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples. Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.

Dynamics -- Congresses. --- Nonlinear control theory. --- Nonlinear systems -- Congresses. --- Nonlinear theories. --- Random dynamical systems. --- Stability. --- Stability -- Congresses. --- Nonlinear systems --- Stability --- System theory --- Economics, Mathematical --- Engineering --- Civil & Environmental Engineering --- Mechanical Engineering --- Engineering & Applied Sciences --- Mechanical Engineering - General --- Operations Research --- Nonlinear systems. --- Systems, Nonlinear --- Engineering. --- System theory. --- Statistical physics. --- Control engineering. --- Economic theory. --- Control. --- Systems Theory, Control. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Nonlinear Dynamics. --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Systems theory. --- Control and Systems Theory. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Physics --- Mathematical statistics --- Systems, Theory of --- Systems science --- Science --- Statistical methods --- Philosophy