Robust stability analysis of uncertain fractional order neutral-type delay nonlinear systems with actuator saturation

Abstract In this paper, we study the robust stability of uncertain fractional order (FO) nonlinear systems having neutral-type delay and input saturation. From the Lyapunov–Krasovskii functional, sufficient criteria on asymptotic robust stability of such FO systems with the help of linear matrix inequalities are specified to compute the gain of state-feedback controller. An optimization is also derived using the cone complementarity linearization method for finding the controller gains subject to maximizing the domain of attraction. The main results are confirmed via numerical examples.

[1]  António M. Lopes,et al.  Multidimensional scaling locus of memristor and fractional order elements , 2020, Journal of advanced research.

[2]  Shaobo Li,et al.  Observer-based adaptive stabilization of the fractional-order chaotic MEMS resonator , 2018 .

[3]  B. Goodwine,et al.  Fractional-order system identification for health monitoring , 2018 .

[4]  Sundarapandian Vaidyanathan,et al.  Dynamic analysis and chaos suppression in a fractional order brushless DC motor , 2017 .

[5]  K. M. Owolabi High-dimensional spatial patterns in fractional reaction-diffusion system arising in biology , 2020 .

[6]  Wei Jiang,et al.  Lyapunov stability analysis of fractional nonlinear systems , 2016, Appl. Math. Lett..

[7]  Jianquan Lu,et al.  Global exponential stability for quaternion-valued recurrent neural networks with time-varying delays , 2016, Nonlinear Dynamics.

[8]  K P Hadeler,et al.  State-dependent neutral delay equations from population dynamics , 2014, Journal of mathematical biology.

[9]  J. A. Tenreiro Machado,et al.  Delay-dependent stability analysis of the QUAD vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks , 2019, Neural Networks.

[10]  Xuefeng Zhang,et al.  Robust stabilization for rectangular descriptor fractional order interval systems with order 0 α  , 2020, Appl. Math. Comput..

[11]  Catherine Bonnet,et al.  H∞-Stability Analysis of Fractional Delay Systems of Neutral Type , 2016, SIAM J. Control. Optim..

[12]  Y. Chen,et al.  Fractional-order model and experimental verification for broadband hysteresis in piezoelectric actuators , 2019, Nonlinear Dynamics.

[13]  Jinde Cao,et al.  Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays , 2014, Nonlinear Dynamics.

[14]  Ping Zhou,et al.  Stabilization of a fractional-order chaotic brushless DC motor via a single input , 2015 .

[15]  Young-Hun Lim,et al.  Stability and Stabilization of Fractional-Order Linear Systems Subject to Input Saturation , 2013, IEEE Transactions on Automatic Control.

[16]  Fernando Tadeo,et al.  Robust stabilization using LMI techniques of neutral time-delay systems subject to input saturation , 2017 .

[17]  Jinde Cao,et al.  Stability and synchronization of fractional-order memristive neural networks with multiple delays , 2017, Neural Networks.

[18]  J. A. Tenreiro Machado,et al.  Lyapunov method for the stability analysis of uncertain fractional-order systems under input saturation , 2020 .

[19]  Peng Wan,et al.  Periodically intermittent control strategies for $$\varvec{\alpha }$$α-exponential stabilization of fractional-order complex-valued delayed neural networks , 2018 .

[20]  Bin Xiao,et al.  Fractional discrete Tchebyshev moments and their applications in image encryption and watermarking , 2020, Inf. Sci..

[21]  Haipeng Peng,et al.  Finite-time projective synchronization of memristor-based delay fractional-order neural networks , 2017 .

[22]  Xiaona Song,et al.  Adaptive hybrid fuzzy output feedback control for fractional-order nonlinear systems with time-varying delays and input saturation , 2020, Appl. Math. Comput..

[23]  José António Tenreiro Machado,et al.  Uniform stability of Fractional Order Leaky Integrator Echo State Neural Network with multiple time delays , 2017, Inf. Sci..

[24]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[25]  Fuzhen Zhang The Schur complement and its applications , 2005 .

[26]  I. Petersen A stabilization algorithm for a class of uncertain linear systems , 1987 .

[27]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

[28]  Sehraneh Ghaemi,et al.  Optimal synchronization of fractional-order chaotic systems subject to unknown fractional order, input nonlinearities and uncertain dynamic using type-2 fuzzy CMAC , 2017, Nonlinear Dynamics.

[29]  José António Tenreiro Machado,et al.  Stability analysis of fractional Quaternion-Valued Leaky Integrator Echo State Neural Networks with multiple time-varying delays , 2019, Neurocomputing.

[30]  Rajivganthi Chinnathambi,et al.  Stability of fractional-order prey–predator system with time-delay and Monod–Haldane functional response , 2018 .

[31]  Fernando O. Souza,et al.  Imaginary characteristic roots of neutral systems with commensurate delays , 2019, Syst. Control. Lett..

[32]  Mahdi Sojoodi,et al.  Robust stabilisation of fractional-order interval systems via dynamic output feedback: an LMI approach , 2018, Int. J. Syst. Sci..

[33]  Michael Pecht,et al.  A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors , 2018, Journal of Power Sources.

[34]  Philipp Hövel,et al.  Control of Complex Nonlinear Systems with Delay , 2010 .

[35]  Alireza Alfi,et al.  Finite-time H∞ control of uncertain networked control systems with randomly varying communication delays. , 2017, ISA transactions.

[36]  J. A. Tenreiro Machado,et al.  Stability analysis of a class of nonlinear fractional‐order systems under control input saturation , 2018 .

[37]  A new parameterization for the concentration flux using the fractional calculus to model the dispersion of contaminants in the Planetary Boundary Layer , 2018, Physica A: Statistical Mechanics and its Applications.

[38]  José António Tenreiro Machado,et al.  Delay independent robust stability analysis of delayed fractional quaternion-valued leaky integrator echo state neural networks with QUAD condition , 2019, Appl. Math. Comput..

[39]  Jun-Guo Lu,et al.  Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities , 2020, Appl. Math. Comput..

[40]  K. Mukdasai,et al.  A Novel Delay-Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation , 2020, Mathematics.

[41]  Xiaoqin Zeng,et al.  Dynamical behavior and synchronization in time-delay fractional-order coupled neurons under electromagnetic radiation , 2018, Nonlinear Dynamics.

[42]  Shiping Wen,et al.  Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks , 2020, Inf. Sci..

[43]  Long-Yeu Chung,et al.  Global Exponential Stability for Uncertain Delayed Neural Networks of Neutral Type With Mixed Time Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[44]  Keum-Shik Hong,et al.  Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation , 2015 .

[45]  M. Rivero,et al.  Fractional calculus: A survey of useful formulas , 2013, The European Physical Journal Special Topics.

[46]  Federico Milano,et al.  On the Stability Analysis of Systems of Neutral Delay Differential Equations , 2018, Circuits, Systems, and Signal Processing.

[47]  B. R. Pontes,et al.  Statements on chaos control designs, including a fractional order dynamical system, applied to a “MEMS” comb-drive actuator , 2012 .

[48]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[49]  Ahmed Alsaedi,et al.  Global Mittag-Leffler stability analysis of impulsive fractional-order complex-valued BAM neural networks with time varying delays , 2020, Commun. Nonlinear Sci. Numer. Simul..

[50]  D. Baleanu,et al.  New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator , 2019, The European Physical Journal Plus.