Sufficient stability condition for fractional-order nonlinear systems

Shao, Keyong; Zuo, Lei

doi:10.1007/s12206-017-0641-z

Cited by 1 publication

(4 citation statements)

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“…This method was extended for stability (check the works of Mahmoud et al 25 and Shao and Zuo 26 ) and observer-based control of the class of No-FOSs, 27 respectively. Similar to the stability analysis approaches based on Lyapunov's direct methods in other works, [19][20][21][22][23][24] the stability conditions of Mahmoud et al, 25 Shao and Zuo, 26 and Qiu and Ji 27 are only true for 0 < < 1 and they are independent of .…”

Section: Introductionmentioning

confidence: 78%

“…Using Schur complement, one can easily show that (30) and (31) are equivalent. This means that our proposed LMI condition (26), without restricting the matrix X to be real and has a special structure, leads to a bigger space solution than the LMI condition of Liu et al 19 In other words, our proposed method is less conservative than the one of Liu et al 19…”

Section: Stability Analysis Via Lmi Conditionsmentioning

confidence: 97%

“…and g(t, x(t)) is a nonlinear Lipschitz function vector with Lipschitz constant L. By solving the LMI (26) in Theorem 3 in MATLAB ® , the largest Lipschitz constant such that guarantees the stability of system (47) is depicted in Figure 2.…”

Section: Example 1 Consider the Following No-fosmentioning

confidence: 99%

“…19 It should be noted that similar conclusion is obtained when we compare our method in Theorem 2 with -independent methods in other works. [20][21][22][23][24][25][26][27] The similar procedure for stability test of system (47) for 1.5 < < 2 is performed and the result is depicted in Figure 4. It is noted that by -independent methods, [19][20][21][22][23][24][25][26][27]…”

Section: Example 2 Consider Another No-fos Asmentioning

confidence: 99%

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Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

Tavazoei

Asemani

2018

Intl J Robust & Nonlinear

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This paper focuses on proposing novel conditions for stability analysis and stabilization of the class of nonlinear fractional-order systems. First, by considering the class of nonlinear fractional-order systems as a feedback interconnection system and applying small-gain theorem, a condition is proposed for L 2 -norm boundedness of the solutions of these systems. Then, by using the Mittag-Leffler function properties, we show that satisfaction of the proposed condition proves the global asymptotic stability of the class of nonlinear fractional-order systems with fractional order lying in (0.5, 1) or (1.5, 2). Unlike the Lyapunov-based methods for stability analysis of fractional-order systems, the new condition depends on the fractional order of the system. Moreover, it is related to the H ∞ -norm of the linear part of the system and it can be transformed to linear matrix inequalities (LMIs) using fractional-order bounded-real lemma. Furthermore, the proposed stability analysis method is extended to the state-feedback and observer-based controller design for the class of nonlinear fractional-order systems based on solving some LMIs. In the observer-based stabilization problem, we prove that the separation principle holds using our method and one can find the observer gain and pseudostate-feedback gain in two separate steps. Finally, three numerical examples are provided to demonstrate the advantage of the novel proposed conditions with the previous results. KEYWORDSH ∞ -norm, nonlinear control, nonlinear fractional-order system, observer-based stabilization, pseudostate feedback Int J Robust Nonlinear Control. 2018;28:4549-4564. wileyonlinelibrary.com/journal/rnc

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