Loading...

 

What is it about?

Lyapunov functions are an outstanding tool for the stability analysis of distributed parameter systems. In the applications, in these systems often terms that model friction effects appear. In the pde literature such terms are referred to as source terms. In this paper we present new Lyapunov functions that are particualrly suitable for the stability analysis of such systems. They have weights that are given by hyperbolic functions and generalize the exponential weights that have been used successfully in particular by Georges Bastin, Jean-Michel Coron, D'Andrea Novel and their collaborators.

Featured Image

Why is it important?

In many applications the most accurate models are given by distributed parameter systems. Stability is of utmost importance in the operation of complex systems. Therefore it is important to develop further methods for the stability analysis of such systems, in order to design new efficient feedback control laws.

Perspectives

Sorry, your browser does not support inline SVG.

In this contribution we have presented weights for Lyapunov functions that are defined as specific hyperbolic functions. In a more abstract setting, it makes sense to look for optimal Lyapunov functions that yield maximal decay rates. Such an approach would lead to sharper results concerning the decay rates. However, the price to pay is that the weights would be much more abstract.

Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg

Read the Original

This page is a summary of: New Lyapunov functions for systems with source terms, Control and Cybernetics, January 2025, De Gruyter,
DOI: 10.2478/candc-2024-0008.
You can read the full text:

Read

Contributors

The following have contributed to this page