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Bounded real lemmas for fractional order systems

Shu Liang, Yi-Heng Wei, Jin-Wen Pan, Qing Gao, Yong Wang
2015 International Journal of Automation and Computing  
This paper derives the bounded real lemmas corresponding to L∞ norm and H∞ norm (L-BR and H-BR) of fractional order systems.  ...  From this advantage, we further address the synthesis problem of H∞ control for fractional order systems in the form of LMI.  ...  Zeng Liao for their suggestive help on this research, and Dr. Xi Zhou for pointing out some mistakes in the previous version of this paper.  ... 
doi:10.1007/s11633-014-0868-4 fatcat:2kkdfbx5xncbffyiqfl5qb6izm

Reduced-order H∞ filtering for commensurate fractional-order systems

Jun Shen, James Lam, Ping Li
2013 52nd IEEE Conference on Decision and Control  
Based on the bounded real lemma for commensurate fractional-order systems, a sufficient condition is established in terms of linear matrix inequalities (LMls) under which the stability as well as the H  ...  This paper is concerned with the reduced-order H= filtering problem of commensurate fractional-order systems.  ...  Fortunately, the bounded real lemma for commensurate fractional-order systems was established in [15] .  ... 
doi:10.1109/cdc.2013.6760568 dblp:conf/cdc/ShenLL13 fatcat:fuqt6jm27fepxb42uq3nvn32ii

Robust Nonfragile Controllers Design for Fractional Order Large-Scale Uncertain Systems with a Commensurate Order1<α<2

Jianyu Lin
2015 Mathematical Problems in Engineering  
Based on the stability criterion of fractional order system, sufficient conditions on the decentralized stabilization of fractional order large-scale uncertain systems in both cases of additive and multiplicative  ...  The paper concerns the problem of stabilization of large-scale fractional order uncertain systems with a commensurate order1<α<2under controller gain uncertainties.  ...  The idea is mainly based on the geometric analysis of a fractional system stability domain. Based on Lemma 5, the stability domain for a fractional order 1 < < 2 is convex.  ... 
doi:10.1155/2015/206908 fatcat:wxkx3n5fgfbdndp5mguesu4lwi

A universal framework of GKYP lemma for singular fractional order systems [article]

Yuman Li, Yiheng Wei, Yuquan Chen, Yong Wang
2019 arXiv   pre-print
Then the bounded real lemma in the sense of L is derived for different frequency ranges.  ...  In this paper, a universal framework of finite frequency band GKYP lemma for singular fractional order systems is established.  ...  L ∞ BOUNDED REAL LEMMAS FOR THE SFOS In this section, the L ∞ bound real lemmas for the SFOS in different frequency ranges will be derived.  ... 
arXiv:1901.07260v1 fatcat:y3y22bmusrbrtkzwrj3v3omxdq

Robust stability and stabilization of LTI fractional-order systems with poly-topic and two-norm bounded uncertainties

Sulan Li
2018 Advances in Difference Equations  
This paper investigates the problems of robust stability and stabilization of LTI fractional-order systems with poly-topic and two-norm bounded uncertainties.  ...  Firstly, some sufficient conditions of the robust asymptotical stable for such fractional-order uncertain systems are derived. Secondly, the robust stabilizing state-feedback controller is designed.  ...  The significance of fractional-order representation is that it is more adequate to describe real world systems than those of integer-order models [2] .  ... 
doi:10.1186/s13662-018-1542-x fatcat:im6tsv7lgfdqtafocthlgiudk4

New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems

Omar Kahouli, Assaad Jmal, Omar Naifar, Abdelhameed M. Nagy, Abdellatif Ben Makhlouf
2022 Mathematics  
In this paper, a novel lemma for the analysis of a function with a bounded Katugampola fractional integral is presented and proven.  ...  In the last few years, a new class of fractional-order (FO) systems, known as Katugampola FO systems, has been introduced.  ...  In this paper, we present a Barbalat-like lemma for the class of Katugampola fractional-order systems.  ... 
doi:10.3390/math10111814 fatcat:en2cqn62ynardcrdjyudtjopde

Stability for Caputo Fractional Differential Systems

Sung Kyu Choi, Bowon Kang, Namjip Koo
2014 Abstract and Applied Analysis  
We introduce the notion ofh-stability for fractional differential systems.  ...  Then we investigate the boundedness andh-stability of solutions of Caputo fractional differential systems by using fractional comparison principle and fractional Lyapunov direct method.  ...  [7] obtained some results about stability of solutions for fractional-order dynamic systems using fractional Lyapunov direct method and fractional comparison principle.  ... 
doi:10.1155/2014/631419 fatcat:gj3s4ine6rcnfdhkew5oaqxuz4

Robust stability bounds of uncertain fractional-order systems

YingDong Ma, Jun-Guo Lu, WeiDong Chen, YangQuan Chen
2014 Fractional Calculus and Applied Analysis  
AbstractThis paper considers the robust stability bound problem of uncertain fractional-order systems.  ...  The fact that these bounds are not exceeded guarantees that the asymptotical stability of the uncertain fractional-order systems is preserved when the nominal fractional-order systems are already asymptotically  ...  Acknowledgements This work was partially supported by the National Natural Science Foundation of China under Grants 60974002, 61221003 and 61374030, and the Research Foundation for the Doctoral Program  ... 
doi:10.2478/s13540-014-0159-3 fatcat:pg37imabyvaszepphuv3b2rnmu

Analysis of a Fractional-Order Couple Model with Acceleration in Feelings

Ilknur Koca, Nuri Ozalp
2013 The Scientific World Journal  
A fractional-order nonlinear dynamical model of couple has been introduced. Upper bounds are obtained for a fractional-order nonlinear dynamical model.  ...  By using stability analysis on fractional-order system, we obtain sufficient condition on the parameters for the locally asymptotic stability of equilibrium points.  ...  Now, with an application of Lemma 8 to (37) combining with (33), upper bounds for a fractional-order nonlinear system are obtained.  ... 
doi:10.1155/2013/730736 pmid:24396305 pmcid:PMC3875104 fatcat:zci3nv7jmjb3hlzy4hzsjyl75e

A New Sufficient Condition for Checking the Robust Stabilization of Uncertain Descriptor Fractional-Order Systems

Hongxing Wang, Aijing Liu
2018 Journal of Function Spaces  
We derive a sufficient condition for the system with the fractional-order α satisfying 1≤α<2 in terms of linear matrix inequalities (LMIs).  ...  The condition of the proposed stability criterion for fractional-order system is easy to be verified. An illustrative example is given to show that our result is effective.  ...  [29] study the robust stability and stabilization of fractional-order linear systems with positive real uncertainty.  ... 
doi:10.1155/2018/4980434 fatcat:rpitf3qoabayxapc3spm3qrzge

SYNTHESIS OF COMPLETE ORTHONORMAL FRACTIONAL BASIS FUNCTIONS WITH PRESCRIBED POLES

Hüseyin Akçay
2007 IFAC Proceedings Volumes  
This presents an extension of the completeness results for the fractional Laguerre and Kautz bases to fractional orthonormal bases with prescribed pole locations.  ...  For a range of noninteger differentiation orders and under mild restrictions on the choice of the basis poles, the synthesized basis functions are shown to be complete in the space of functions which are  ...  This means that the system defined by (4) with for all maps bounded energy inputs to bounded energy outputs .  ... 
doi:10.3182/20070822-3-za-2920.00131 fatcat:pg32ei2kobhtxdxyvgayimvy3a

Synthesis of Complete Orthonormal Fractional Basis Functions With Prescribed Poles

H. Akcay
2008 IEEE Transactions on Signal Processing  
This presents an extension of the completeness results for the fractional Laguerre and Kautz bases to fractional orthonormal bases with prescribed pole locations.  ...  For a range of noninteger differentiation orders and under mild restrictions on the choice of the basis poles, the synthesized basis functions are shown to be complete in the space of functions which are  ...  This means that the system defined by (4) with for all maps bounded energy inputs to bounded energy outputs .  ... 
doi:10.1109/tsp.2008.928163 fatcat:4ttjgfja3bg2vewunywcgq5adi

On bounded real lemma for fractional systems

Mathieu Moze, Jocelyn Sabatier, Alain Oustaloup
2008 IFAC Proceedings Volumes  
Prospects of this study are in the fields covered by the usual bounded real lemma such as ∞ H control, thus aiming at straightforward extension to fractional systems.  ...  Its formulation is similar to the well known bounded real lemma whereas it does not guarantee stability.  ...  Theorem 2 is an extension of the bounded real lemma for fractional systems. It enables computation of a fractional system L 2 -gain from its state-space "like" representation.  ... 
doi:10.3182/20080706-5-kr-1001.02582 fatcat:n3hjaztwnndpteyvcx3qxku4wy

Robust Synchronization Controller Design for a Class of Uncertain Fractional Order Chaotic Systems

Lin Wang, Chunzhi Yang
2016 Discrete Dynamics in Nature and Society  
Synchronization problem for a class of uncertain fractional order chaotic systems is studied.  ...  Some fundamental lemmas are given to show the boundedness of a complicated infinite series which is produced by differentiating a quadratic Lyapunov function with fractional order.  ...  This result is given to use for stability analysis of fractional order nonlinear systems, especially for Mittag-Leffler stability [2] analysis of fractional order nonlinear systems. Lemma 6.  ... 
doi:10.1155/2016/2090583 fatcat:fe4pmv56tbhkbkjehmsjrnym5u

Existence and Uniqueness of Positive and Bounded Solutions of a Discrete Population Model with Fractional Dynamics

J. E. Macías-Díaz
2017 Discrete Dynamics in Nature and Society  
Positive and bounded initial-boundary data are imposed on a closed and bounded domain, and a fully discrete form of this fractional initial-boundary-value problem is provided next using fractional centered  ...  Using this fact, we establish that the discrete population model is capable of preserving the positivity and the boundedness of the discrete initial-boundary conditions.  ...  For example, it would be interesting to determine whether theorems on the existence and the uniqueness of positive and bounded solutions for more general discrete fractional systems can be established.  ... 
doi:10.1155/2017/5716015 fatcat:44efafqwuvb3xn4x6stugczbui
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