Robust Stability and Stabilization of Fractional Order Systems Based on Uncertain Takagi-Sugeno Fuzzy Model With the Fractional Order 1≤v < 2

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Li Junmin ◽  
Li Yuting
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Stability And Stabilization ◽  
Takagi Sugeno ◽  
Robust Stability And Stabilization

This paper addresses the problems of the robust stability and stabilization for fractional order systems based on the uncertain Takagi-Sugeno fuzzy model. A sufficient and necessary condition of asymptotical stability for fractional order uncertain T-S fuzzy model is given, and a parallel distributed compensate fuzzy controller is designed to asymptotically stabilize the model. The results are obtained in terms of linear matrix inequalities. Finally, a numerical example and fractional order Van der Pol system are given to show the effectiveness of our results.

scholarly journals Robust Stability and Stabilization of Interval Uncertain Descriptor Fractional-Order Systems with the Fractional-Orderα: The1≤α<2Case

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yuanhua Li ◽  
Heng Liu ◽  
Hongxing Wang
Keyword(s):  
Fractional Order ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Interval System ◽  
Interval Coefficients ◽  
Stability And Stabilization ◽  
Necessary And Sufficient ◽  
Robust Stability And Stabilization

Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimensionnonly need to solve one 4n-by-4nLMI. Numerical examples are presented to shown the effectiveness of our results.

Robust stability and stabilization of uncertain fractional order systems subject to input saturation

2017 ◽  
Vol 24 (16) ◽  
pp. 3676-3683 ◽  
Author(s):  
Esmat Sadat Alaviyan Shahri ◽  
Alireza Alfi ◽  
JA Tenreiro Machado
Keyword(s):  
Fractional Order ◽  
Robust Stability ◽  
State Feedback ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
Stability And Stabilization ◽  
The Stability ◽  
Robust Stability And Stabilization

This paper studies the stability and the stabilization for a class of uncertain fractional order (FO) systems subject to input saturation. The Lipschitz condition and the Gronwall–Bellman lemma are adopted and sufficient conditions are derived to stabilize systems by designing a state feedback controller. Numerical examples demonstrate the effectiveness of the proposed method.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

scholarly journals Further results on robust fuzzy dynamic systems with LMI D-stability constraints

2014 ◽  
Vol 24 (4) ◽  
pp. 785-794 ◽  
Author(s):  
Wudhichai Assawinchaichote
Keyword(s):  
Dynamic Systems ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Local System ◽  
Linear Matrix ◽  
Fuzzy Modelling ◽  
Ts Fuzzy Model ◽  
Input Noise ◽  
Takagi Sugeno

Abstract This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

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