EE 857 Nonlinear Control Systems 
Spring 2007

Instructor: Prof. Andrea Serrani.
Office: 412 Dreese Lab. (email:

Course Schedule:  Monday, Wednesday, Friday 9:30am-10:18am 135 Caldwell Labs .

This is a new graduate course within the control area. It aims at providing the necessary background for advanced analysis and control of nonlinear systems. The course will emphasize recent as well as classical techniques and methodologies for designing control systems for complex, interconnected nonlinear systems. Classical results in the stabilization of nonlinear systems will also be treated in detail. Applications of nonlinear control design ranging from aerospace to robotics will be considered throughout the course.

Prerequisites: EE 754 Nonlinear systems.

Textbook and useful references:

(PLEASE NOTE: Although no official textbook will be followed in this course, the book by Khalil can be used to cover large portions of the material.  Notes and selected journal papers will be made available throughout the course).

Homework 40% , Take-home final (Project) 60%.


Course outline
  1. Input-Output and Input-to-State stability of nonlinear systems. Sontag's input-to-state stability. Definitions and Lyapunov-like characterizations. Feedback equivalence and input-to-state stabilizability of nonlinear systems. Input-to-state stability of cascade systems. Design examples. 
  1. Dissipative systems. L2 - gain and passivity theory. Dissipative and zero-state detectable systems. Finite L2-gain systems, and associated small-gain theorem. Passive systems and passive interconnections. Feedback equivalence to a passive systems. Examples.
  1. Stability of interconnected nonlinear systems. The small-gain theorem for ISS systems. Robust stabilization. Design examples.
  1. Global stabilization for nonlinear systems in normal form. Backstepping techniques. Control Lyapunov functions. Sontag-Artstein formula.
  1.  Semi-global stabilization of nonlinear systems in normal form. Bacciotti's theorem on "potentially global" stabilization. The peaking phenomenon. Robust semi-global stabilization: the Teel-Praly construction. Design examples.
  1. Tracking and regulation in nonlinear systems: the Isidori-Byrnes regulator. Examples

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