October 27, 2009, 10:00 - 11:00 am
117 Electrical Engineering Building

Constructions of Strict Lyapunov Functions: An Overview

Mathematical control theory provides the theoretical foundations that undergird many modern technologies, including aeronautics, biotechnology, communications networks, manufacturing, and models of climate change. During the past fifteen years, there have been numerous exciting developments at the interface of control engineering and mathematical control theory. Many of these advances were based on new Lyapunov methods for analyzing and stabilizing nonlinear systems. Constructing strict Lyapunov functions is a central and challenging problem.  Even when we know a system to be globally asymptotically stable, it is often still important to have an explicit global strict Lyapunov function, e.g., to design feedbacks that give input-to-state stability to actuator errors.

 

Once we construct a suitable global strict Lyapunov function, several significant stabilization and robustness problems can be solved almost immediately, using standard arguments.  The simplicity of our strict Lyapunov function constructions makes them suitable for quantifying the effects of uncertainty, and for feedback design.

 

Presented by:

Michael Malisoff, Associate Professor, LSU Department of Mathematics

 

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