Reset control systems: the zero-crossing resetting law

TL;DR

This paper introduces a new hybrid systems framework for reset control with zero-crossing laws, analyzing well-posedness and stability using eigenstructure and Lyapunov methods, addressing non-deterministic behaviors in control systems.

Contribution

It presents a novel hybrid inclusion model for reset control systems with zero-crossing laws, and develops stability conditions based on eigenstructure and Lyapunov functions.

Findings

Established well-posedness criteria for the hybrid reset control systems.

Derived stability conditions using eigenstructure analysis.

Proposed Lyapunov-based stability criteria for the systems.

Abstract

A novel representation of reset control systems with a zero-crossing resetting law, in the framework of hybrid inclusions, is postulated. The problems of well-posedness and stability of the resulting hybrid dynamical system are investigated, with a strong motivation in how non-deterministic behavior is accomplished in control practice. Several stability conditions, based on the eigenstructure of matrices related with periods of the reset interval sequences, and on Lyapunov function-based conditions, are developed.