{"product_id":"nonlinear-systems-9781292039213","title":"Nonlinear Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e 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.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAll chapters conclude with \u003ci\u003eExercises\u003c\/i\u003e. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e1. Introduction.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eNonlinear Models and Nonlinear Phenomena. Examples. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e2. Second-Order Systems.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eQualitative Behavior of Linear Systems. Multiple Equilibria. Qualitative Behavior Near Equilibrium Points. Limit Cycles. Numerical Construction of Phase Portraits. Existence of Periodic Orbits. Bifurcation. Systems. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e3. Fundamental Properties.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eExistence and Uniqueness. Continuos Dependence on Initial Conditions and Parameters. Differentiability of solutions and Sensitivity Equations. Comparison Principle. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e4. Lyapunov Stability.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eAutonomous Systems. The Invariance Principle. Linear Systems and Linearization. Comparison Functions. Nonautonomous Systems. Linear Time-Varying Systems and Linearization. Converse Theorems. Boundedness and Ultimate Boundedness. Input-to-State Stability. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e5. Input-Output Stability.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003e \u003ci\u003eL\u003c\/i\u003e Stability. \u003ci\u003eL\u003c\/i\u003e Stability of State Models. \u003ci\u003eL\u003c\/i\u003e2 Gain. Feedback Systems: The Small-Gain Theorem. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e6. Passivity.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eMemoryless Functions. State Models. Positive Real Transfer Functions. \u003ci\u003eL\u003c\/i\u003e2 and Lyapunov Stability. Feedback Systems: Passivity Theorems. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e7. Frequency-Domain Analysis of Feedback Systems.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eAbsolute Stability. The Describing Function Method. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e8. Advanced Stability Analysis.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eThe Center Manifold Theorem. Region of Attraction. Invariance-like Theorems. Stability of Periodic Solutions. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e9. Stability of Perturbed Systems.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eVanishing Pertubation. Nonvanishing Pertubation. Comparison Method. Continuity of Solutions on the Infinite Level. Interconnected Systems. Slowly Varying Systems. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e10. Perturbation Theory and Averaging.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eThe Perturbation Method. Perturbation on the Infinite Level. Periodic Perturbation of Autonomous Systems. Averaging. Weekly Nonlinear Second-Order Oscillators. General Averaging. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e11. Singular Perturbations.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eThe Standard Singular Perturbation Model. Time-Scale Properties of the Standard Model. Singular Perturbation on the Infinite Interval. Slow and Fast Manifolds. Stability Analysis. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e12. Feedback Control.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eControl Problems. Stabilization via Linearization. Integral Control. Integral Control via Linearization. Gain Scheduling. \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e13. Feedback Linearization.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eMotivation. Input-Output Linearization. Full-State Linearization. State Feedback Control. \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eIndex.\u003c\/b\u003e \u003cbr\u003e\u003c\/p\u003e","brand":"Pearson Education Limited","offers":[{"title":"Default Title","offer_id":48866510700887,"sku":"9781292039213","price":76.94,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781292039213.jpg?v=1722279007","url":"https:\/\/bookcurl.com\/products\/nonlinear-systems-9781292039213","provider":"Book Curl","version":"1.0","type":"link"}