5B5770 Nonlinear Systems Analysis

Instructor: Xiaoming Hu

Literature: Lecture notes will be handed out. You can download the lecture notes here (Password required). For further reading: Nonlinear systems (2nd edition) by H. Khalil, published by Prentice-Hall, ISBN is 0-13-228024-8.

Intended Audience: Graduate Students in applied mathematics and engineering. Senior undergraduate students are also welcome.

Goal: This course is a basic course on nonlinear dynamical systems, presented from systems and control point of view. The main difference from the course Introduction to Nonlinear ControlSystems is: in that course, the synthesis or control design of nonlinear control systems is emphasized; and in this course, the analysis tools are studied. we plan to cover a range of topics on nonlinear systems such as approximation methods, periodic solutions, Liapunov stability, input-output stability and nonsmooth systems. If the previous course is more control oriented, I hope this course would appeal to a wider range of audience.

Examination: One is required to do the homework assignments and to pass the open-book final exam.

Course Plan:

There are about 12 lectures (two hours each). Each of the following chapters will be covered by one or several lectures:

• Nonlinear Differential Systems: basic definitions, existence of solution, maximal solutions, global existence and uniqueness, autonomous systems, some differential inequalities and second order systems
• Periodic Solutions
• Liapunov Stability: preliminaries, stability of linear systems, principle of stability in the 1st approximation and Liapunov direct method.
• Advanced Topics in Liapunov Stability: LaSalle's theorem, global stability and converse theorems.
• Stability of Invariant Set and Model Reduction: stability of invariant set, center manifold and singular perturbation.
• Analysis of Input-Output Systems: input-output stability, describing function methods, the Lur'e problem.
• Nonsmooth systems and switching systems: solution and stability of such systems.

Lectures: 13:00-15:00 every Tuesday (starting Feb. 3, 2004), at Room 3721, Lindstedtsv 25.

Please send me an email to register and to receive course information later.