First graduate level course in nonlinear systems. Introduction to nonlinear phenomena: multiple equilibria, limit cycles, bifurcations, complex dynamical behavior. Planar dynamical systems, analysis using phase plane techniques. Describing functions. Input-output analysis and stability. Lyapunov stability theory. The Lure problem, Circle and Popov criterion. Feedback linearization, sliding mode control. The course will be punctuated by a rich set of examples, ranging from violin strings to jet engines, from heart beats to artificial neurons, and from population growth to nonlinear flight control.
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Control Systems (E205); Linear Algebra (Math. 103, 113); Exposure to
Exposure to MATLAB is strongly recommended.
The course is based on a set of lecture notes which will be made available
throughout the term.
The following are reference texts which are available in the bookstore.
S. S. Sastry. Nonlinear Systems: Analysis, Stability, and Control. Springer-Verlag, 1999. We will be covering topics from Chapters 1, 2, 5, 9, 10, and selected topics from Chapters 3, 4, and 6.
H. K. Khalil. Nonlinear Systems, 3rd Edition. Prentice-Hall, 2002. The relevant Chapters are 1, 2, 4, 12, 13, 14, and selected topics from 3, 5, 7, 8.