Robust admissibility and stabilization of uncertain singular fractional-order linear time-invariant systems

2019 ◽  
Vol 6 (3) ◽  
pp. 685-692 ◽  
Author(s):  
Saliha Marir ◽  
Mohammed Chadli
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Robust Controllability of Interval Fractional Order Linear Time Invariant Systems

2005 ◽  
Author(s):  
Yang Quan Chen ◽  
Hyo-Sung Ahn ◽  
Dingyu¨ Xue
Keyword(s):  
State Space ◽  
Fractional Order ◽  
Linear Time ◽  
Interval Uncertainty ◽  
State Matrix ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Robust Controllability ◽  
Time Invariant

We consider uncertain fractional-order linear time invariant (FO-LTI) systems with interval coefficients. Our focus is on the robust controllability issue for interval FO-LTI systems in state-space form. We re-visited the controllability problem for the case when there is no interval uncertainty. It turns out that the stability check for FO-LTI systems amounts to checking the conventional integer order state space using the same state matrix A and the input coupling matrix B. Based on this fact, we further show that, for interval FO-LTI systems, the key is to check the linear dependency of a set of interval vectors. Illustrative examples are presented.

Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Jun-Guo Lu ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Stability Condition ◽  
Linear Time ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Matrix Variable ◽  
Stability And Stabilization ◽  
Linear Time Invariant Systems ◽  
Time Invariant ◽  
Convex Polytopic Uncertainties

AbstractThis paper considers the problems of robust stability and stabilization for a class of fractional-order linear time-invariant systems with convex polytopic uncertainties. The stability condition of the fractional-order linear time-invariant systems without uncertainties is extended by introducing a new matrix variable. The new extended stability condition is linear with respect to the new matrix variable and exhibits a kind of decoupling between the positive definite matrix and the system matrix. Based on the new extended stability condition, sufficient conditions for the above robust stability and stabilization problems are established in terms of linear matrix inequalities by using parameter-dependent positive definite matrices. Finally, numerical examples are provided to illustrate the proposed results.

scholarly journals Tuning of a time-delayed controller for a general class of second-order linear time invariant systems with dead-time

2019 ◽  
Vol 13 (3) ◽  
pp. 451-457 ◽  
Author(s):  
Raul Villafuerte-Segura ◽  
Francisco Medina-Dorantes ◽  
Leopoldo Vite-Hernández ◽  
Baltazar Aguirre-Hernández
Keyword(s):  
General Class ◽  
Dead Time ◽  
Linear Time ◽  
Second Order ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

scholarly journals Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 136
Author(s):  
Manuel Duarte-Mermoud ◽  
Javier Gallegos ◽  
Norelys Aguila-Camacho ◽  
Rafael Castro-Linares
Keyword(s):  
Fractional Order ◽  
Performance Optimization ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Minimal Realization ◽  
Linear Time Invariant ◽  
Mixed Order ◽  
Linear Time Invariant Systems ◽  
Minimal Realizations ◽  
Time Invariant

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.

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