Modeling and stability analysis of live systems with time-varying dimension

TL;DR

This paper introduces a framework for analyzing the stability of systems with a changing number of states over time, extending classical control methods to more dynamic, real-world systems.

Contribution

It proposes a novel framework for live systems with time-varying dimensions and extends stability analysis tools like Lyapunov methods to this setting.

Findings

Input-to-state stability is suitable for live systems.

Classical control tools can be adapted for systems with changing state spaces.

The framework applies to multi-agent systems, industrial processes, and smart grids.

Abstract

A major limitation of the classical control theory is the assumption that the state space and its dimension do not change with time. This prevents analyzing and even formalizing the stability and control problems for open multi-agent systems whose agents may enter or leave the network, industrial processes where the sensors or actuators may be exchanged frequently, smart grids, etc. In this work, we propose a framework of live systems that covers a rather general class of systems with a time-varying state space. We argue that input-to-state stability is a proper stability notion for this class of systems, and many of the classic tools and results, such as Lyapunov methods and superposition theorems, can be extended to this setting.