Signal Sets on Time Scales with Application to Hybrid Systems

TL;DR

This paper extends time scales calculus to define signal sets and their stability, providing a unified framework for analyzing hybrid systems with generalized Lyapunov conditions.

Contribution

It introduces the concept of signal sets on time scales and develops stability criteria, enhancing modeling and analysis of hybrid systems.

Findings

Unified approach to hybrid systems analysis

Generalized Lyapunov stability conditions

Flexible modeling of hybrid trajectories

Abstract

Recently, time scales calculus is developed to unify continuous and discrete analysis. By extending the definition of time scales properly, this paper introduces the concept of a signal set as well as its stability properties in terms of the so-called pseudo distance measure. This leads to more general Lyapunov like conditions to check stability properties of systems with hybrid nature. By way of examples, the proposed framework is used to model hybrid systems with simplicity and flexibility to characterize trajectories in the behavior of hybrid systems.