55 research outputs found
(R1517) Asymptotical Stability of Riemann-Liouville Fractional Neutral Systems with Multiple Time-varying Delays
In this manuscript, we investigate the asymptotical stability of solutions of Riemann-Liouville fractional neutral systems associated to multiple time-varying delays. Then, we use the linear matrix inequality (LMI) and the Lyapunov-Krasovskii method to obtain sufficient conditions for the asymptotical stability of solutions of the system when the given delays are time dependent and one of them is unbounded. Finally, we present some examples to indicate the efficacy of the consequences obtained
A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent
asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and
Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National
Research Council of Thailand and Khon Kaen University, Thailand (6200069)
A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation
The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent
asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and
Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National
Research Council of Thailand and Khon Kaen University, Thailand (6200069)
On the Asymptotic Stability of a Nonlinear Fractional-order System with Multiple Variable Delays
In this paper, we consider a nonlinear differential system of fractional-order with multiple variable delays. We investigate asymptotic stability of zero solution of the considered system. We prove a new result, which includes sufficient conditions, on the subject by means of a suitable Lyapunov functional. An example with numerical simulation of its solutions is given to illustrate that the proposed method is flexible and efficient in terms of computation and to demonstrate the feasibility of established conditions by MATLAB-Simulink
Stability and stabilization of fractional order time delay systems
U ovom radu predstavljeni su neki osnovni rezultati koji se odnose na kriterijume stabilnosti sistema necelobrojnog reda sa kaÅ”njenjem kao i za sisteme necelobrojnog reda bez kaÅ”njenja.TakoÄe, dobijeni su i predstavljeni dovoljni uslovi za konaÄnom vremenskom stabilnost i stabilizacija za (ne)linearne (ne)homogene kao i za perturbovane sisteme necelobrojnog reda sa vremenskim kaÅ”njenjem. Nekoliko kriterijuma stabilnosti za ovu klasu sistema necelobrojnog reda je predloženo koriÅ”Äenjem nedavno dobijene generalizovane Gronval nejednakosti, kao i 'klasiÄne' Belman-Gronval nejednakosti. Neki zakljuÄci koji se odnose na stabilnost sistema necelobrojnog reda su sliÄni onima koji se odnose na klasiÄne sisteme celobrojnog reda. Na kraju, numeriÄki primer je dat u cilju ilustracije znaÄaja predloženog postupka.In this paper, some basic results of the stability criteria of fractional order system with time delay as well as free delay are presented. Also, we obtained and presented sufficient conditions for finite time stability and stabilization for (non)linear (non)homogeneous as well as perturbed fractional order time delay systems. Several stability criteria for this class of fractional order systems are proposed using a recently suggested generalized Gronwall inequality as well as 'classical' Bellman-Gronwall inequality. Some conclusions for stability are similar to those of classical integerorder differential equations. Finally, a numerical example is given to illustrate the validity of the proposed procedure
Stability of fractional order time delay systems
In this paper, some basic results of the stability criteria of fractional order system
with time delay as well as free delay are presented. Also, they are obtained and presented
sufficient conditions for finite time stability for (non)linear (non)homogeneous as well as
perturbed fractional order time delay systems. Several stability criteria for this class of
fractional order systems are proposed using a recently suggested generalized Gronwall
inequality as well as āclassicalā Bellman-Gronwall inequality. Some conclusions for
stability are similar to that of classical integer-order differential equations. Last, a numerical
example is given to illustrate the validity of the proposed procedure
Observer-Based Robust Controller Design for Nonlinear Fractional-Order Uncertain Systems via LMI
We discuss the observer-based robust controller design problem for a class of nonlinear fractional-order uncertain systems with admissible time-variant uncertainty in the case of the fractional-order satisfying 0<Ī±<1. Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer-based nonlinear fractional-order uncertain systems is presented. Employing Finslerās Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations
Stability analysis of visco-elastically damped structure through Bagley Torvik Equation
The stability of fractional-order visco-elastically damped linear system Bagley Torvik equation is analyzed in this paper. The fundamental novelty of this paper is the application of Caputo derivative. Prevailing sufficient spectral conditions are considered to guarantee the stability of linear models. Laplace transform, and Mittag-Leffler functions are utilized to develop the results. Furthermore, asymptotical stability of linear fractional-order models are also achieved through spectral values of the characteristic polynomials. Numerical examples are given to display the effectiveness of suggested method
Multi-weighted complex structure on fractional order coupled neural networks with linear coupling delay: a robust synchronization problem
This sequel is concerned with the analysis of robust synchronization for a multi-weighted complex structure on fractional-order coupled neural networks (MWCFCNNs) with linear coupling delays via state feedback controller. Firstly, by means of fractional order comparison principle, suitable Lyapunov method, Kronecker product technique, some famous inequality techniques about fractional order calculus and the basis of interval parameter method, two improved robust asymptotical synchronization analysis, both algebraic method and LMI method, respectively are established via state feedback controller. Secondly, when the parameter uncertainties are ignored, several synchronization criterion are also given to ensure the global asymptotical synchronization of considered MWCFCNNs. Moreover, two type of special cases for global asymptotical synchronization MWCFCNNs with and without linear coupling delays, respectively are investigated. Ultimately, the accuracy and feasibility of obtained synchronization criteria are supported by the given two numerical computer simulations.This article has been written with the joint financial support of RUSA-Phase 2.0 grant sanctioned vide letter No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, UGC-SAP (DRS-I) vide letter No.F.510/8/DRSI/2016(SAP-I) and DST (FIST - level I) 657876570 vide letter No.SR/FIST/MS-I/2018/17
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