The BRADLEY DEPARTMENT of ELECTRICAL and COMPUTER ENGINEERING

# ECE 5774 Nonlinear Systems Theory | ECE | Virginia Tech

### Course Information

#### Description

Introduction to the theory of systems of coupled, nonlinear, time-varying ordinary differential equations: existence and uniqueness of solutions; continuous dependence on parameters; stability of equilibria and stability analysis techniques; input-to-state stability; input-output stability; nonlinear control design techniques including input-state and input-output feedback linearization, backstepping, and sliding mode control.

#### Why take this course?

Nonlinear systems theory provides a theoretical framework for studying a large class of systems that are not amenable to linear systems techniques. Moreover, nonlinear techniques can strengthen conclusions about the behavior of those systems which are amenable to linear analysis. Nonlinear systems theory also forms the basis for a variety of nonlinear control design methods that can improve closed-loop performance and robustness beyond the capabilities of linear control design methods.

#### Prerequisites

ECE 4405 or ECE 4624 or ECE 4634 or ME 4504 or AOE 4004.

### Major Measurable Learning Objectives

• State and assess conditions for local and global existence and uniqueness of solutions of a nonlinear time-varying state equation.
• Apply Lyapunov's direct and indirect methods for determing stability of equilibria.
• Apply advanced stability analysis techniques, including Lasalle's invariance principle and Barbalat's lemma.
• Define the L2-gain of a system and use the small-gain theorem to assess stability of a feedback interconnection.
• Determine whether a given system can be linearized through state or output feedback and apply these techniques.
• Determine whether a given system can be controlled through backstepping or sliding mode control and apply these techniques.

### Course Topics

#### Percentage of Course

1. Nonlinear System Analysis - Existence and uniqueness of solutions; continuous dependence on parameters; stability of equilibria and analysis techniques. 25%
2. Control System Properties - Input-to-state stability, input-output stability, L2gain, small gain theorem 25%
3. Control Design Techniques. %
a. Input-state linearization 20%
b. Input-output linearization 10%
c. Sliding mode control, backstepping, advanced topics 20%