Stability Analysis of Linear Time-Invariant Distributed-Order Systems

TL;DR

This paper establishes stability conditions for linear time-invariant distributed-order systems over the interval (0,1), providing analytical time-domain responses and numerical validation for different weighting functions.

Contribution

It introduces the first stability conditions for LTI distributed-order systems over (0,1) and analyzes two cases of weighting functions with analytical and numerical methods.

Findings

Derived necessary and sufficient stability conditions.

Provided analytical time-domain responses.

Validated conditions with numerical examples.

Abstract

Bounded-input bounded-output stability condition of linear time invariant (LTI) distributed-order system over integral interval $(0,1)$ has been established for the first time. Two cases about weighting function of the distributed order are investigated, and sufficient and necessary conditions of stability for these two types of distributed-order systems are derived. Based on the complex integration analysis, time-domain responses of distributed-order systems are also given by analytical method, and numerical examples are presented to illustrate the proposed conditions.