Sub-Optimum H2 Rational Approximations to Fractional Order Linear Systems

In this paper, we propose a procedure to achieve rational approximation to arbitrary fractional order linear time invariant (FO-LTI) systems with sub-optimum H2-norm. Through illustrations, we show that the rational approximation is simple and effective. It is also demonstrated that this sub-optimum approximation method is effective in designing integer order controllers for FO-LTI systems in general form. Useful Matlab codes are also given in the appendices.

Suboptimum H2 Pseudo-rational Approximations to Fractional-order Linear Time Invariant Systems

Advances in Fractional Calculus ◽

10.1007/978-1-4020-6042-7_5 ◽

2007 ◽

pp. 61-75 ◽

Cited By ~ 9

Author(s):

Dingyü Xue ◽

YangQuan Chen

Keyword(s):

Fractional Order ◽

Linear Time ◽

Rational Approximations ◽

Order Linear ◽

Linear Time Invariant ◽

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

Open Physics ◽

10.2478/s11534-013-0274-5 ◽

2013 ◽

Vol 11 (6) ◽

Cited By ~ 1

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 ◽

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.

The FCC Stability Criterion for Fractional-Order Linear Time-Invariant Systems with Commensurate or Incommensurate Orders

2018 Annual American Control Conference (ACC) ◽

10.23919/acc.2018.8431868 ◽

2018 ◽

Author(s):

Arman Dabiri ◽

Eric A. Butcher

Keyword(s):

Fractional Order ◽

Stability Criterion ◽

Linear Time ◽

Order Linear ◽

Linear Time Invariant ◽

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

IEEE/CAA Journal of Automatica Sinica ◽

10.1109/jas.2019.1911480 ◽

2019 ◽

Vol 6 (3) ◽

pp. 685-692 ◽

Cited By ~ 3

Author(s):

Saliha Marir ◽

Mohammed Chadli

Keyword(s):

Fractional Order ◽

Linear Time ◽

Order Linear ◽

Linear Time Invariant ◽

Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

Robust Controllability of Interval Fractional Order Linear Time Invariant Systems

10.1115/detc2005-84744 ◽

2005 ◽

Cited By ~ 14

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 ◽

Robust Controllability ◽

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 of fractional-order linear time-invariant systems with multiple noncommensurate orders

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2011.10.014 ◽

2012 ◽

Vol 64 (10) ◽

pp. 3053-3058 ◽

Cited By ~ 14

Author(s):

Zhuang Jiao ◽

Yang Quan Chen

Keyword(s):

Fractional Order ◽

Linear Time ◽

Order Linear ◽

Linear Time Invariant ◽

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

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-013-0010-2 ◽

2013 ◽

Vol 16 (1) ◽

Cited By ~ 26

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 ◽

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.

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

Entropy ◽

10.3390/e20060400 ◽

2018 ◽

Vol 20 (6) ◽

pp. 400 ◽

Cited By ~ 7

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 ◽

Robust controllability of interval fractional order linear time invariant stochastic systems

2012 IEEE 51st IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc.2012.6425949 ◽

2012 ◽

Author(s):

Caibin Zeng ◽

YangQuan Chen ◽

Qigui Yang

Keyword(s):

Fractional Order ◽

Stochastic Systems ◽

Linear Time ◽

Order Linear ◽

Linear Time Invariant ◽

Robust Controllability ◽

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

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4026042 ◽

2014 ◽

Vol 9 (3) ◽

Cited By ~ 2

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.