Nonlinear SystemsThis book is written is such a way that the level of mathematical sophistication builds up from chapter to chapter. It has been reorganized into four parts: basic analysis, analysis of feedback systems, advanced analysis, and nonlinear feedback control. Updated content includes subjects which have proven useful in nonlinear control design in recent years-- new in the 3rd edition are: expanded treatment of passivity and passivity-based control; integral control, high-gain feedback, recursive methods, optimal stabilizing control, control Lyapunov functions, and observers. For use as a self-study or reference guide by engineers and applied mathematicians. |
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analysis apply approach approximation assume asymptotically stable averaged behavior bounded Chapter choose circle closed closed-loop system conclude condition connection Consider continuously differentiable defined dependent derivative describing eigenvalues equation equilibrium point error estimate Example Exercise existence exponentially stable fact Figure finite given globally Hence hold Hurwitz inequality initial input integration interval invariant Lemma limit linear system Lipschitz Lyapunov function manifold mapping matrix method negative neighborhood nominal nonlinear nonlinear system obtain origin oscillation parameters periodic solution perturbation perturbed system phase portrait plane positive constants positive definite problem proof properties reduced reference region of attraction represented requirement respect satisfies Show shown solution solving starting sufficiently Suppose t₁ term Theorem trajectories uniformly variables vector x(to zero მუ