Basic Properties of Singular Fractional Order System with order (1,2)

TL;DR

This paper investigates key properties of singular fractional order systems with order between 1 and 2, including regularity, stability, and admissibility, providing theoretical conditions and numerical solutions.

Contribution

It introduces new necessary and sufficient conditions for stability and admissibility of SFOS with fractional order between 1 and 2.

Findings

Established a necessary and sufficient condition for stability.

Proved multiple conditions for admissibility.

Provided a numerical example illustrating the conditions.

Abstract

This paper focuses on some properties, which include regularity, impulse, stability, admissibility and robust admissibility, of singular fractional order system (SFOS) with fractional order $1<\alpha<2$. The finitions of regularity, impulse-free, stability and admissibility are given in the paper. Regularity is analysed in time domain and the analysis of impulse-free is based on state response. A sufficient and necessary condition of stability is established. Three different sufficient and necessary conditions of admissibility are proved. Then, this paper shows how to get the numerical solution of SFOS in time domain. Finally, a numerical example is provided to illustrate the proposed conditions.