On the robustness of hybrid control systems to measurement noise and actuator disturbances

TL;DR

This paper investigates the robustness of hybrid control systems against noise and disturbances, highlighting the gap between theoretical robustness and practical implementation, and proposing a new concept of strong robustness with sufficient conditions.

Contribution

It introduces the concept of strong robustness for hybrid control systems and provides conditions ensuring robustness of practical implementations.

Findings

Weak robustness does not guarantee implementation robustness.

Strong robustness ensures robustness of jumping-first and flowing-first implementations.

A sufficient condition for strong robustness is established.

Abstract

Robustness of hybrid control systems to measurement noise, actuator disturbances, and more generally perturbations, is analyzed. The relationship between the robustness of a hybrid control system and of its implementations is emphasized. Firstly, a formal definition of implementation of a hybrid control system is provided, based on the uniqueness of the solutions. Then, two examples are analyzed in detail, showing how the previously developed robustness property fails to guarantee that the implementations, necessarily used in control practice, are also robust. A new concept of strong robustness is proposed, which guarantees that at least jumping-first and flowing-first implementations are robust when the hybrid control system is strongly robust. In addition, we provide a sufficient condition for strong robustness based on the previously developed hybrid relaxation results.