Nonlinear Dynamical Systems
A textbook for a graduate or senior course in control or electrical engineering or mathematics. Presents methods for understanding nonlinear systems, keeping the mathematics fairly elementary. The second edition adds references at the end of each chapter, more exercises, and several new topics. No date is noted for the first edition. Annotation copyright by Book News, Inc., Portland, OR
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Describing Function Analysis
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adaptive control analysis applied approach approximation assumed becomes boundary bounded chaotic behaviour coefficients components control law control system converge corresponding dead zone define denote depend describing function describing function method DIDF differential equation discontinuous dither dither signal domain of attraction dynamical system eigenvalues equilibrium point error signal Example feedback loop feedback system Fourier Fourier series frequency G(ico given gives globally asymptotically stable hence illustrated in Figure input-output relation integral intersection limit cycle limit cycle conditions linear element linear system Lyapunov exponents Lyapunov function nonlinear element nonlinear function nonlinear system Nyquist plot obtain oscillation output parameter period phase plane phase portrait Poincare-Bendixson theorem positive constants positive-real possible predicted recurrence relation reference input region result satisfied scalar shown in Figure SIDF singular points sinusoidal solution stable limit cycle stable manifold state-space equations state-space representation switching time-invariant transfer function G(s Tsypkin unstable variables vector zero