共查询到17条相似文献,搜索用时 93 毫秒
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提出一种分数阶线性系统稳定性证明方法。首先分析了双参数Mittag-Leffler函数估值定理中的限制条件, 通过证明得出了该定理收敛域有误, 因此改进了双参数Mittag-Leffler函数估值定理, 并将它的参数由实数推广到矩阵。然后提出了可适用于分数阶线性系统的稳定性理论, 并利用改进的双参数Mittag-Leffler函数估值定理进行了证明。仿真结果验证了理论的正确性。 相似文献
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主要对一类范数有界参数的分数阶线性控制系统,研究了使闭环系统全局渐进稳定的静态输出反馈控制器的设计问题。以线性矩阵不等式(LMI)的形式,证明了上述不确定系统的全局渐进稳定问题,等价于求一个线性矩阵不等式的可行解问题,并且利用该线性矩阵不等式的可行解,构造出了上述系统输出反馈控制器。 相似文献
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分数阶系统的分数阶PID控制器设计 总被引:9,自引:1,他引:9
对于一些复杂的实际系统,用分数阶微积分方程建模要比整数阶模型更简洁准确.分数阶微积分也为描述动态过程提供了一个很好的工具.对于分数阶模型需要提出相应的分数阶控制器来提高控制效果.本文针对分数阶受控对象,提出了一种分数阶PID控制器的设计方法.并用具体实例演示了对于分数阶系统模型,采用分数阶控制器比采用古典的PID控制器取得更好的效果. 相似文献
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Omar Naifar A. M. Nagy Abdellatif Ben Makhlouf Mohamed Kharrat Mohamed Ali Hammami 《国际强度与非线性控制杂志
》2019,29(1):180-187
》2019,29(1):180-187
In this paper, a finite‐time stability results of linear delay fractional‐order systems is investigated based on the generalized Gronwall inequality and the Caputo fractional derivative. Sufficient conditions are proposed to the finite‐time stability of the system with the fractional order. Numerical results are given and compared with other published data in the literature to demonstrate the validity of the proposed theoretical results. 相似文献
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A Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order
systems is presented via an auxiliary integer degree polynomial. The presented Routh test is a classical Routh table test on the
auxiliary integer degree polynomial derived from and for the commensurate fractional degree polynomial. The theoretical proof
of this proposed approach is provided by utilizing Argument principle and Cauchy index. Illustrative examples show efficiency
of the presented approach for stability test of commensurate fractional degree polynomials and commensurate fractional order
systems. So far, only one Routh-type test approach [1] is available for the commensurate fractional degree polynomials in the
literature. Thus, this classical Routh-type test approach and the one in [1] both can be applied to stability analysis and design for
the fractional order systems, while the one presented in this paper is easy for peoples, who are familiar with the classical Routh
table test, to use. 相似文献
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A note on the stability of fractional order systems 总被引:1,自引:0,他引:1
In this paper, a new approach is suggested to investigate stability in a family of fractional order linear time invariant systems with order between 1 and 2. The proposed method relies on finding a linear ordinary system that possesses the same stability property as the fractional order system. In this way, instead of performing the stability analysis on the fractional order systems, the analysis is converted into the domain of ordinary systems which is well established and well understood. As a useful consequence, we have extended two general tests for robust stability check of ordinary systems to fractional order systems. 相似文献
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This paper considers the finite‐time stability of fractional order impulsive switched systems. First, by using the fractional order Lyapunov function, Mittag–Leffler function, and Gronwall–Bellman lemma, two sufficient conditions are given to verify the finite‐time stability of fractional order nonlinear systems. Then, the concept of finite‐time stability is extended to fractional order impulsive switched systems. A sufficient condition is given to verify the finite‐time stability of fractional order impulsive switched systems by combining the method of average dwell time with fractional order Lyapunov function. Finally, two numerical examples are provided to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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In this paper, the Arnoldi-based model reduction methods are employed to fractional order linear time-invariant systems. The resulting model has a smaller dimension, while its fractional order is the same as that of the original system. The error and stability of the reduced model are discussed. And to overcome the local convergence of Padé approximation, the multi-point Arnoldi algorithm, which can recursively generate a reduced-order orthonormal basis from the corresponding Krylov subspace, is used. Numerical examples are given to illustrate the accuracy and efficiency of the proposed methods. 相似文献
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Dorota Mozyrska Ewa Pawłuszewicz Małgorzata Wyrwas 《International journal of systems science》2017,48(4):788-794
The concepts of local controllability and observability of nonlinear discrete-time systems with the Caputo-, Riemann–Liouville- and Grünwald–Letnikov-type h-difference fractional order operators are studied. The Implicit Function Theorem is used in order to show that the nonlinear systems are locally observable or controllable in a finite number of steps if their linear approximations are observable or controllable, respectively, in the same number of steps. 相似文献
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The componentwise asymptotic stability (CWAS) and componentwise exponential asymptotic stability (CWEAS) represent stronger types of asymptotic stability, which were first defined for symmetrical bounds constraining the flow of the state‐space trajectories, and then, were generalized for arbitrary bounds, not necessarily symmetrical. Our paper explores the links between the symmetrical and the general case, proving that the former contains all the information requested by the characterization of the CWAS/CWEAS as qualitative properties. Complementary to the previous approaches to CWAS/CWEAS that were based on the construction of special operators, we incorporate the flow‐invariance condition into the classical framework of stability analysis. Consequently, we show that the componentwise stability can be investigated by using the operator defining the system dynamics, as well as the standard ε?δ formalism. Although this paper explicitly refers only to continuous‐time linear systems, the key elements of our work also apply, mutatis mutandis, to discrete‐time linear systems. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献