Nonlinear Systems

Inbunden, Engelska, 2002

AvHassan Khalil

5 659 kr

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For a first-year graduate-level course on nonlinear systems. It may also be used for self-study or reference by engineers and applied mathematicians. The text is written to build the level of mathematical sophistication from chapter to chapter. It has been reorganized into four parts: Basic analysis, Analysis of feedback systems, Advanced analysis, and Nonlinear feedback control.

Produktinformation

Utgivningsdatum2002-01-18
Mått187 x 241 x 32 mm
Vikt1 220 g
FormatInbunden
SpråkEngelska
Antal sidor768
Upplaga3
FörlagPearson Education
ISBN9780130673893

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All chapters conclude with Exercises.1. Introduction Nonlinear Models and Nonlinear PhenomenaExamples2. Second-Order Systems Qualitative Behavior of Linear SystemsMultiple EquilibriaQualitative Behavior Near Equilibrium PointsLimit CyclesNumerical Construction of Phase PortraitsExistence of Periodic OrbitsBifurcationSystems3. Fundamental Properties Existence and UniquenessContinuous Dependence on Initial Conditions and ParametersDifferentiability of solutions and Sensitivity EquationsComparison Principle4. Lyapunov Stability Autonomous SystemsThe Invariance PrincipleLinear Systems and LinearizationComparison FunctionsNonautonomous SystemsLinear Time-Varying Systems and LinearizationConverse TheoremsBoundedness and Ultimate BoundednessInput-to-State Stability5. Input-Output Stability L StabilityL Stability of State ModelsL2 GainFeedback Systems: The Small-Gain Theorem6. Passivity Memoryless FunctionsState ModelsPositive Real Transfer FunctionsL2 and Lyapunov StabilityFeedback Systems: Passivity Theorems7. Frequency-Domain Analysis of Feedback Systems Absolute StabilityThe Describing Function Method8. Advanced Stability Analysis The Center Manifold TheoremRegion of AttractionInvariance-like TheoremsStability of Periodic Solutions9. Stability of Perturbed Systems Vanishing PertubationNonvanishing PertubationComparison MethodContinuity of Solutions on the Infinite LevelInterconnected SystemsSlowly Varying Systems10. Perturbation Theory and Averaging The Perturbation MethodPerturbation on the Infinite LevelPeriodic Perturbation of Autonomous SystemsAveragingWeekly Nonlinear Second-Order OscillatorsGeneral Averaging11. Singular Perturbations The Standard Singular Perturbation ModelTime-Scale Properties of the Standard ModelSingular Perturbation on the Infinite IntervalSlow and Fast ManifoldsStability Analysis12. Feedback Control Control ProblemsStabilization via LinearizationIntegral Control. Integral Control via LinearizationGain Scheduling13. Feedback Linearization MotivationInput-Output LinearizationFull-State LinearizationState Feedback Control14. Nonlinear Design Tools Sliding Mode ControlLyapunov RedesignBacksteppingPassivity-Based ControlHigh-Gain ObserversAPPENDICES A. Mathematical ReviewB. Contraction MappingC. Proofs.Notes and References