*-Continuous Kleene $\omega$-Algebras

TL;DR

This paper introduces *-continuous Kleene ω-algebras, exploring their properties and demonstrating their application in solving energy problems in hybrid systems.

Contribution

It defines *-continuous Kleene ω-algebras and shows their connection to iteration semiring-semimodule pairs, with applications to hybrid system energy problems.

Findings

Establishment of properties of *-continuous Kleene ω-algebras

Connection to iteration semiring-semimodule pairs

Application to energy problems in hybrid systems

Abstract

We define and study basic properties of *-continuous Kleene $\omega$-algebras that involve a *-continuous Kleene algebra with a *-continuous action on a semimodule and an infinite product operation that is also *-continuous. We show that *-continuous Kleene $\omega$-algebras give rise to iteration semiring-semimodule pairs. We show how our work can be applied to solve certain energy problems for hybrid systems.