Lur'e dynamical systems with state-dependent set-valued feedback

TL;DR

This paper introduces an implicit discretization scheme to establish the existence and uniqueness of strong solutions for Lur'e dynamical systems with state-dependent set-valued feedback, enhancing numerical simulation capabilities.

Contribution

It generalizes previous work by addressing strong solutions and implicit discretization for systems with state-dependent set-valued feedback, including time-varying cases.

Findings

Established existence and uniqueness of strong solutions.

Provided conditions for exponential attractivity.

Extended results to systems with data errors.

Abstract

Using a new implicit discretization scheme, we study in this paper the existence and uniqueness of strong solutions for a class of Lur'e dynamical systems where the set-valued feedback depends on both time and state. This work is a generalization of \cite{abc} where the time-dependent set-valued feedback is considered to acquire only weak solutions. Obviously, strong solutions and implicit discretization scheme are nice properties, especially for numerical simulation. We also provide some conditions such that the solutions are exponentially attractive. The obtained results can be used to study the time-varying Lur'e systems with errors in data. Our result is new even the set-valued feedback depends only on the time.