Asymptotic Stabilization for a Class of Linear Fractional-Order Composite Systems
Zhe Zhang*, Toshimitsu Ushio**, Jing Zhang*, Feng Liu***, and Can Ding*
*College of Electrical and Information Engineering, Hunan University
Changsha, Hunan 410082, China
**Graduate School of Engineering Science, Osaka University
1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
***School of Automation, China University of Geosciences
388 Lumo Road, Hongshan District, Wuhan 430074, China
In this paper, we present the design for a decentralized control method comprising a series of local state feedback controllers for a class of linear fractional composite systems. In addition, the corresponding asymptotic stabilization criterion is derived. First, we design the local state feedback controllers for each subsystem of the linear fractional composite system. Then, based on the vector Lyapunov function, we combine these local state feedback controllers into a single decentralized controller through which the asymptotic stabilization criterion is proposed for the class of linear fractional composite system. Finally, numerical simulation of a class of linear fractional composite systems is used to verify the accuracy and effectiveness of the decentralized control method.
-  M. Messadi and A. Mellit, “Control of chaos in an induction motor system with LMI predictive control and experimental circuit validation,” Chaos, Solitons & Fractals, Vol.97, pp. 51-58, 2017.
-  H. Liu, S. Li, G. Li et al., “Robust adaptive control for fractional-order financial chaotic systems with system uncertainties and external disturbances,” Information Technology & Control, Vol.46, No.2, 2017.
-  R. Almeida, “A Caputo fractional derivative of a function with respect to another function,” Communications in Nonlinear Science & Numerical Simulation, Vol.44, pp. 460-481, 2017.
-  D. Baleanu, G.-C. Wu, and S.-D. Zeng, “Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations,” Chaos Solitons & Fractals, Vol.102, pp. 99-105, 2017.
-  B. Bao, N. Wang, M. Chen et al., “Inductor-free simplified Chua’s circuit only using two-op-amp-based realization,” Nonlinear Dynamics, Vol.84, No.2, pp. 511-525, 2016.
-  R. Rocha, J. Ruthiramoorthy, and T. Kathamuthu, “Memristive oscillator based on Chua’s circuit: stability analysis and hidden dynamics,” Nonlinear Dynamics, Vol.88, No.4, pp. 2577-2587, 2017.
-  J. Kengne, “On the Dynamics of Chua’s oscillator with a smooth cubic nonlinearity: occurrence of multiple attractors,” Nonlinear Dynamics, Vol.87, pp. 363-375, 2017.
-  Z. Zhang, J. Zhang, and Z. Ai, “A novel stability criterion of the time-lag fractional-order gene regulatory network system for stability analysis,” Communications in Nonlinear Science & Numerical Simulation, Vol.66, pp. 96-108, 2019.
-  O. Guner, “Exp-Function Method and Fractional Complex Transform for Space-Time Fractional KP-BBM Equation,” Communications in Theoretical Physics, Vol.68, No.2, pp. 149-154, 2017.
-  W. S. Chung, S. Zare, and H. Hassanabadi, “Investigation of Conformable Fractional Schrödinger Equation in Presence of Killingbeck and Hyperbolic Potentials,” Communications in Theoretical Physics, Vol.67, No.3, pp. 250-254, 2017.
-  S. M. A. Pahnehkolaei, A. Alfi, and J. A. T. Machado, “Dynamic stability analysis of fractional order leaky integrator echo state neural networks,” Communications in Nonlinear Science & Numerical Simulation, Vol.47, pp. 328-337, 2017.
-  K. Zhang, H. Wang, and H. Fang, “Feedback control and hybrid projective synchronization of a fractional-order Newton–Leipnik system,” Communications in Nonlinear Science and Numerical Simulation, Vol.17, No.1, pp. 317-328, 2012.
-  D. D. Siljak, “Decentralized control of complex systems,” Academic Press, 2012.
-  K. Fukuda and T. Ushio, “Decentralized Event-Triggered Control of Composite Systems Using M-Matrices,” IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, Vol.101, No.8, pp. 1156-1161, 2018.
-  Y. Li, Y. Q. Chen, and I. Podlubny, “Mittag–Leffler stability of fractional order nonlinear dynamic systems,” Automatica, Vol.45, pp. 1965-1969, 2009.
-  H. T. Tuan and H. Trinh, “Stability of fractional-order nonlinear systems by Lyapunov direct method,” IET Control Theory & Applications, Vol.12, No.17, pp. 2417-2422, 2018.