scholarly journals The General Solution of Singular Fractional-Order Linear Time-Invariant Continuous Systems with Regular Pencils

Entropy ◽  
2018 ◽  
Vol 20 (6) ◽  
pp. 400 ◽  
Author(s):  
Iqbal Batiha ◽  
Reyad El-Khazali ◽  
Ahmed AlSaedi ◽  
Shaher Momani
Keyword(s):  
General Solution ◽  
Fractional Order ◽  
Linear Time ◽  
Continuous Systems ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Time Invariant

Fractional-order linear time invariant swarm systems: asymptotic swarm stability and time response analysis

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Mojtaba Soorki ◽  
Mohammad Tavazoei
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Time Response ◽  
Response Analysis ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Time Response Analysis ◽  
Necessary And Sufficient ◽  
Time Invariant

AbstractThis paper deals with fractional-order linear time invariant swarm systems. Necessary and sufficient conditions for asymptotic swarm stability of these systems are presented. Also, based on a time response analysis the speed of convergence in an asymptotically swarm stable fractional-order linear time invariant swarm system is investigated and compared with that of its integer-order counterpart. Numerical simulation results are presented to show the effectiveness of the paper results.

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.

Adaptive Consensus Tracking for Fractional-Order Linear Time Invariant Swarm Systems

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Mojtaba Naderi Soorki ◽  
Mohammad Saleh Tavazoei
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Adaptive Controller ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Consensus Tracking ◽  
Simulation Results ◽  
Interactive Dynamics ◽  
Time Invariant ◽  
Adaptive Stabilizer

This paper presents an adaptive controller to achieve consensus tracking for the fractional-order linear time invariant swarm systems in which the matrices describing the agent dynamics and the interactive dynamics between agents are unknown. This controller consists of two parts: an adaptive stabilizer and an adaptive tracker. The adaptive stabilizer guarantees the asymptotic swarm stability of the considered swarm system. Also, the adaptive tracker enforces the system agents to track a desired trajectory while achieving consensus. Numerical simulation results are presented to show the effectiveness of the proposed controller.

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