A graphical approach for stability and robustness analysis in commensurate and incommensurate fractional‐order systems

Abstract

In this paper, a novel graphical approach for stability and robustness analysis in commensurate and incommensurate fractional-order systems (FOS) is proposed. The approach can determine zero distribution of system characteristic equations with commensurate and incommensurate fractional-orders in right-half plane (RHP) and imaginary axis in the complex plane. The approach proposed is derived and generalizd from Routh-type test for polynomials with the commensurate fractional and integer orders. In addition, the novel graphical approach can treat robustness issues of some certain systems. Furthermore, some examples are given to demonstrate the effectiveness of the approach.Finally, a proof is given to verify the correctness of the criterion.

Robust stability analysis of uncertain incommensurate fractional order quasi-polynomials in the presence of interval fractional orders and interval coefficients

“…The stability of (22) has been proved in Shen et al (2020) and Liang et al (2017). Theorem 2 of this paper simply confirms the stability of (22).…”

“…But, Theorem 1 of this paper simply confirms that the fractional order polynomial (21) is stable. Also, consider Example 1 in Liang et al (2017) (or Example 2 in Shen et al (2020)), which is…”

“…The stability analysis of linear time invariant (LTI) fractional order polynomials has been investigated in several studies (Badri and Sojoodi, 2019; Bonnet and Partington, 2002, 2000; Galkowski et al, 2006; Moornani and Haeri, 2010a; Partington and Bonnet, 2004; Rajchakit et al, 2020a, 2020b). Moreover, in some literature (Busłowicz, 2009; Liang et al, 2017; Shen et al, 2020) some graphical procedures have been presented to analyze the stability of fractional order polynomials.…”

Dynamic analysis of a novel time‐lag four‐dimensional fractional‐order financial system

“…It is very important to study the dynamics of complex systems and many scholars have carried out relevant research. [2][3][4][5][6] Elsadany [7] considers that expectations play an important role in modeling economic phenomena, and a producer can choose his expectation rules from many available techniques to adjust his production outputs. In, [8] the stability of a time-delay integer-order financial system using Lyapunov stability theorem is studied.…”

Computation of Stability Criterion for Fractional Shimizu–Morioka System Using Optimal Routh–Hurwitz Conditions

“…Although the Routh-Hurwitz conditions can be considered as an old topic, due to the recent development in fractional calculus, the study of Routh-Hurwitz conditions for fractional systems has emerged recently. Among that are a new Routh-type table for fractional system [17], Routh-Hurwitz-Liénard-Chipart Criteria [18], and a graphical approach to study stability analysis for incommensurate fractional-order systems [19].…”