EEC251 – Nonlinear Systems
3 units – Spring Quarter; alternate years
Lecture: 3 hours
Prerequisite: EEC 250
Grading: Letter; homework.
Nonlinear differential equations, second-order systems, approximation methods, Lyapunov stability, absolute stability, Popov criterion, circle criterion, feedback linearization techniques.
Expanded Course Description:
Basic analysis techniques for nonlinear systems.
- Normed Linear Vector Spaces; Inner Product Spaces
- Cauchy sequences, Banach spaces, Hilbert spaces
- Existence and Uniqueness of Solutions
- Contraction mapping theorem
- Lipschitz condition
- Bellman-Gronwall Lemma
- Small gain theorem
- Nonlinear Differential Equations
- Equilibrium points
- Second-Order Systems
- Phase plane portrait
- Limit cycles
- Bendixson’s theorem
- Poincaré-Bendixson theorem
- Index theory
- Approximation Methods
- Krylov-Baguliubov method
- Describing functions technique, optimal quasilinear
- Lyapunov Stability
- Stable, uniformly stable, attractive, asymptotically stable, globally asymptotically stable equilibrium point
- Class K functions, positive definite functions, decrescent functions, radially unbounded functions
- Derivative along trajectories
- Lyapunov’s direct method
- Invariant set theorems; La Salle’s theorem
- Instability theorems
- Lyapunov stability of linear, time-invariant systems
- Lyapunov’s linearization method
- Krasovskii’s method
- The Luré Problem (Absolute Stability)
- Positive real transfer functions
- Kalman-Yacubovich Lemma
- Aizerman’s conjecture; Kalman’s conjecture
- Circle criterion
- Popov criterion
- Feedback linearization
- Vector fields, forms
- Inverse function theorem; Implicit function theorem
- Lie derivative; Lie bracket
- Complete integrability; involutivity
- Frobenius theorem
- Single-input feedback linearization
- Kronecker indices
- Brunovsky canonical form
- M. Vidyasagar, Nonlinear Systems Analysis, Prentice-Hall, 1992.
- J. J. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, 1991 (recommended).
- Course notes.
THIS COURSE DOES NOT DUPLICATE ANY EXISTING COURSE.
Last revised: December 1991