Analysis and Design of Reset Control Systems via Base Linear Scaled Graphs

TL;DR

This paper introduces a new method using scaled graphs to analyze and design reset control systems, simplifying stability verification by relating it to linear system properties.

Contribution

It establishes a novel stability analysis framework for reset control systems based on scaled graphs, extending to time-regularized resets.

Findings

Scaled graphs of reset systems are bounded by those of base linear systems.

Stability of reset systems can be verified through properties of linear components.

The framework accommodates reset systems with time-regularization.

Abstract

In this letter, we prove that under mild conditions, the scaled graph of a reset control system is bounded by the scaled graph of its underlying base linear system, i.e., the system without resets. Building on this new insight, we establish that the negative feedback interconnection of a linear time-invariant plant and a reset controller is stable, if the scaled graphs of the underlying base linear components are strictly separated. This result simplifies reset system analysis, as stability conditions reduce to verifying properties of linear time-invariant systems. We exploit this result to develop a systematic approach for reset control system design. Our framework also accommodates reset systems with time-regularization, which were not addressed in the context of scaled graphs before.