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This paper deals with the robust control problem for linear systems with both gain and time constants variations under fractional order PIλDμ controller. A robustness specification to the parameters variations is proposed. For those systems with more than one uncertain time constant, the robustness specifications are analyzed and simplified. To minimize the phase offset nearby the crossover frequency,...
By utilizing LDU factorization of high frequency gain (HFG) Kp, a novel fractional order composite model reference adaptive control (MRAC) is investigated for a class of fractional order multi variable systems. Firstly, in the proposed method, the stringent symmetry assumption related with the plant high frequency gain matrix is removed. Besides, by means of fractional order tracking differentiator,...
Inspired by the birth of fractional calculus, this paper ties fractional calculus to L'Hôpital's rule. This yields augmentations of L'Hôpital's rule, for the indeterminate form of type 0/0 and ∞/∞ cases. By mean of the ∊ − δ language, an instructive proof is provided, which can treat the 0/0 and ∞/∞ cases in a parallel fashion. The presented results may evoke a deeper understanding of the limit concept.
This paper investigates the problem pertained to adaptive backstepping control for a class of incommensurate fractional order nonlinear systems. The controlled plant is of parametric strict-feedback form with unknown parameters, varying disturbance and partial measurable state. To solve this problem, a novel state observer is constructed first and then an adaptive control law is developed via the...
In this study, fractional order indirect model reference adaptive control method is used to control a class of fractional order systems. Unlike the traditional integer order case, the controller is obtained by Lyapunov method and the closed-loop stability is achieved via indirect Lyapunov method rather than the certainty equivalence principle. Moreover, for the knowledge that the fractional order...
This paper focuses on the admissibility analysis of singular fractional order systems. A novel stability criterion of normal fractional order systems is introduced first. An essential remark is provided on the distribution of eigenvalue of system matrix. Then a necessary and sufficient condition for the admissibility of singular fractional order systems is derived. All the results are obtained in...
In this paper, a novel approach is presented to approximate the general fractional order nonlinear dynamic systems. Firstly, a generalized T-S fuzzy method is used to approximate the original models. Then a new method to approximate the fractional order T-S models is utilized, and obtain a series of integer order linear model. It is revealed for the first time that a general fractional order nonlinear...
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