Robust Finite-Time Stability and Stabilization of a Class of Fractional-Order Switched Nonlinear Systems

This paper deals with the problem of finite-time boundedness and finite-time stabilization boundedness of fractional-order switched nonlinear systems with exogenous inputs. By constructing a simple Lyapunov-like function and using some properties of Caputo derivative, the authors obtain some new sufficient conditions for the problem via linear matrix inequalities, which can be efficiently solved by using existing convex algorithms. A constructive geometric is used to design switching laws amongst the subsystems. The obtained results are more general and useful than some existing works, and cover them as special cases, in which only linear fractional-order systems were presented. Numerical examples are provided to demonstrate the effectiveness of the proposed results.

[1]  Dongyan Li,et al.  Research on vibration suppression method of alternating current motor based on fractional order control strategy , 2017 .

[2]  Wenhai Qi,et al.  Finite-Time $$L_2$$L2–$$L_\infty $$L∞ Control for Stochastic Asynchronously Switched Systems with Time-Varying Delay and Nonlinearity , 2018, Circuits Syst. Signal Process..

[3]  Yu Xue,et al.  A self-adaptive artificial bee colony algorithm based on global best for global optimization , 2017, Soft Computing.

[4]  Ying-Xu Yang,et al.  Finite‐time stability of fractional order impulsive switched systems , 2015 .

[5]  Shiguo Lian,et al.  Hybrid multiplicative multi-watermarking in DWT domain , 2017, Multidimens. Syst. Signal Process..

[6]  Jun Zhao,et al.  Robust H∞ control for a class of uncertain nonlinear switched systems with average dwell time , 2013, Int. J. Control.

[7]  Inés Tejado,et al.  Stability of fractional order switching systems , 2012, Comput. Math. Appl..

[8]  Chengsheng Yuan,et al.  Fingerprint liveness detection based on multi-scale LPQ and PCA , 2016, China Communications.

[9]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[10]  Hao Liu,et al.  Finite-time stabilization and boundedness of switched linear system under state-dependent switching , 2013, J. Frankl. Inst..

[11]  Xingming Sun,et al.  Structural Minimax Probability Machine , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Manuel A. Duarte-Mermoud,et al.  Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[13]  Weihai Zhang,et al.  State and output feedback finite-time guaranteed cost control of linear itô stochastic systems , 2015, J. Syst. Sci. Complex..

[14]  Francesco Amato,et al.  Input-output finite time stabilization of linear systems , 2010, Autom..

[15]  Bing He,et al.  A novel two-stage hybrid swarm intelligence optimization algorithm and application , 2012, Soft Computing.

[16]  Yuquan Chen,et al.  Fractional‐order multivariable composite model reference adaptive control , 2017 .

[17]  P. Dorato,et al.  Finite time stability under perturbing forces and on product spaces , 1967, IEEE Transactions on Automatic Control.

[18]  Bo Li,et al.  Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment , 2017, Applied Soft Computing.

[19]  Yun Chen,et al.  Finite-Time Stability and Stabilization of Fractional Order Positive Switched Systems , 2016, Circuits, Systems, and Signal Processing.

[20]  Junzhi Yu,et al.  LMI Conditions for Global Stability of Fractional-Order Neural Networks , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Yan Li,et al.  An innovative fractional order LMS based on variable initial value and gradient order , 2017, Signal Process..

[22]  K.N. Salama,et al.  Control and switching synchronization of fractional order chaotic systems using active control technique , 2013, Journal of advanced research.

[23]  Ahmed El Hajjaji,et al.  Stabilization of Continuous-Time Fractional Positive T–S Fuzzy Systems by Using a Lyapunov Function , 2017, Circuits, Systems, and Signal Processing.

[24]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

[25]  Francesco Amato,et al.  Input-output finite-time stability of linear systems , 2009, 2009 17th Mediterranean Conference on Control and Automation.

[26]  Song Liu,et al.  Lyapunov method for nonlinear fractional differential systems with delay , 2015 .

[27]  Hieu Minh Trinh,et al.  Reachable sets bounding for switched systems with time-varying delay and bounded disturbances , 2017, Int. J. Syst. Sci..

[28]  Yue-E Wang,et al.  Finite-time stability and finite-time boundedness of fractional order linear systems , 2016, Neurocomputing.

[29]  Mai Viet Thuan,et al.  New Results on Stabilization of Fractional‐Order Nonlinear Systems via an LMI Approach , 2018 .

[30]  Yun Zou,et al.  Finite-time stability of switched nonlinear systems with finite-time unstable subsystems , 2015, J. Frankl. Inst..

[31]  Xinzhi Liu,et al.  Stability of a class of linear switching systems with time delay , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[32]  Ali Khaki Sedigh,et al.  Sufficient condition for stabilization of linear time invariant fractional order switched systems and variable structure control stabilizers. , 2012, ISA transactions.

[33]  Vu Ngoc Phat,et al.  Switched controller design for stabilization of nonlinear hybrid systems with time-varying delays in state and control , 2010, J. Frankl. Inst..

[34]  Yuanan Liu,et al.  Dual-band coupled-line bandpass filter with independently tunable bandwidths , 2016, China Communications.

[35]  L. Menini,et al.  Dead‐beat regulation of mechanical juggling systems , 2018 .

[36]  Wu Deng,et al.  A novel collaborative optimization algorithm in solving complex optimization problems , 2016, Soft Computing.

[37]  Yun Q. Shi,et al.  An integer wavelet transform based scheme for reversible data hiding in encrypted images , 2018, Multidimens. Syst. Signal Process..

[38]  Yun Zou,et al.  Finite-time stability of switched linear systems with subsystems which are not finite-time stable , 2014 .

[39]  Songsong Cheng,et al.  A universal modified LMS algorithm with iteration order hybrid switching. , 2017, ISA transactions.

[40]  Carlo Cosentino,et al.  Finite-time stabilization via dynamic output feedback, , 2006, Autom..

[41]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[42]  Patrizio Colaneri,et al.  Passivity of switched linear systems: Analysis and control design , 2012, Syst. Control. Lett..

[43]  Rui Yao,et al.  A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm , 2017, Soft Computing.

[44]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[45]  Meng Sun,et al.  A New Feature Extraction Method Based on EEMD and Multi-Scale Fuzzy Entropy for Motor Bearing , 2016, Entropy.

[46]  Guopei Chen,et al.  Stability of a class of nonlinear fractional order impulsive switched systems , 2017 .

[47]  Jingcheng Wang,et al.  Finite time stability and L2-gain analysis for switched linear systems with state-dependent switching , 2013, J. Frankl. Inst..

[48]  Bin Gu,et al.  A Robust Regularization Path Algorithm for $\nu $ -Support Vector Classification , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[49]  B. Jiang,et al.  Stability of fractional-order switched non-linear systems , 2016 .

[50]  Vasily E. Tarasov,et al.  No violation of the Leibniz rule. No fractional derivative , 2013, Commun. Nonlinear Sci. Numer. Simul..

[51]  Anis Sakly,et al.  On the stability analysis of switched nonlinear systems with time varying delay under arbitrary switching , 2017, J. Syst. Sci. Complex..

[52]  Weihua Deng,et al.  Remarks on fractional derivatives , 2007, Appl. Math. Comput..

[53]  S. Ge,et al.  Switched Linear Systems: Control and Design , 2005 .

[54]  Saeed Balochian,et al.  On the Stabilization of Linear Time Invariant Fractional Order Commensurate Switched Systems , 2015 .