Robust stability analysis for fractional‐order systems with time delay based on finite spectrum assignment

2019 ◽  
Vol 29 (8) ◽  
pp. 2283-2295 ◽  
Author(s):  
Lu Liu ◽  
Shuo Zhang ◽  
Dingyu Xue ◽  
YangQuan Chen
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Robust Stability ◽  
Fractional Order Systems ◽  
Finite Spectrum ◽  
Spectrum Assignment ◽  
Robust Stability Analysis

Robust Stability Analysis of Interval Fractional-Order Plants with Interval Time delay and General Form of Fractional-Order Controllers

2021 ◽  
pp. 1-1
Author(s):  
Majid Ghorbani ◽  
Mahsan Tavakoli-Kakhki ◽  
Aleksei Tepljakov ◽  
Eduard Petlenkov ◽  
Arash Farnam ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Robust Stability ◽  
Interval Time ◽  
Robust Stability Analysis

scholarly journals Robust Stability of Fractional Order Time-Delay Control Systems: A Graphical Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Radek Matušů ◽  
Roman Prokop
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Robust Stability ◽  
Irrigation Canal ◽  
Graphical Approach ◽  
Delay Term ◽  
Integer Order ◽  
Robust Stability Analysis ◽  
Value Sets

The paper deals with a graphical approach to investigation of robust stability for a feedback control loop with an uncertain fractional order time-delay plant and integer order or fractional order controller. Robust stability analysis is based on plotting the value sets for a suitable range of frequencies and subsequent verification of the zero exclusion condition fulfillment. The computational examples present the typical shapes of the value sets of a family of closed-loop characteristic quasipolynomials for a fractional order plant with uncertain gain, time constant, or time-delay term, respectively, and also for combined cases. Moreover, the practically oriented example focused on robust stability analysis of main irrigation canal pool controlled by either classical integer order PID or fractional order PI controller is included as well.

scholarly journals Robust Stability Analysis of Nonlinear Fractional-Order Time-Variant Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Chen Caixue ◽  
Xie Yunxiang
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Robust Stability ◽  
State Feedback ◽  
Stability Theorem ◽  
Feedback Controller ◽  
Sufficient Condition ◽  
Fractional Order Systems ◽  
Numerical Example ◽  
Robust Stability Analysis

This paper presents a stability theorem for a class of nonlinear fractional-order time-variant systems with fractional orderα  (1<α<1)by using the Gronwall-Bellman lemma. Based on this theorem, a sufficient condition for designing a state feedback controller to stabilize such fractional-order systems is also obtained. Finally, a numerical example demonstrates the validity of this approach.

Robust Stability Analysis of Uncertain Linear Fractional-Order Systems With Time-Varying Uncertainty for 0 < α < 2

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Mohammad Tavazoei ◽  
Mohammad Hassan Asemani
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Robust Stability ◽  
Stability Condition ◽  
Upper Bound ◽  
Order System ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Robust Stability Analysis ◽  
The Stability

This paper focuses on the stability analysis of linear fractional-order systems with fractional-order 0<α<2, in the presence of time-varying uncertainty. To obtain a robust stability condition, we first derive a new upper bound for the norm of Mittag-Leffler function associated with the nominal fractional-order system matrix. Then, by finding an upper bound for the norm of the uncertain fractional-order system solution, a sufficient non-Lyapunov robust stability condition is proposed. Unlike the previous methods for robust stability analysis of uncertain fractional-order systems, the proposed stability condition is applicable to systems with time-varying uncertainty. Moreover, the proposed condition depends on the fractional-order of the system and the upper bound of the uncertainty matrix norm. Finally, the offered stability criteria are examined on numerical uncertain linear fractional-order systems with 0<α<1 and 1<α<2 to verify the applicability of the proposed condition. Furthermore, the stability of an uncertain fractional-order Sallen–Key filter is checked via the offered condition.

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