Global Exponential Stability and Stabilization of Fractional-Order Positive Switched Systems

Authors

  • Xiangyang Cao College of Information Engineering, Henan University of Science and Technology, Luoyang, China, Author
  • Leipo Liu College of Information Engineering, Henan University of Science and Technology, Luoyang, China, Author

Keywords:

fractional-order positive switched systems, global exponential stability, average dwell time

Abstract

This paper is concerned with the global  exponential stability(GES) and stabilization of  fractional-order positive switched systems(FOPSS) with  average dwell time(ADT). Firstly, the the concept of  GES is extended to FOPSS. Then, by constructing  copositive Lyapunov functions and using ADT  approach, a state feedback controller is constructed,  and sufficient conditions are derived to guarantee that  the corresponding closed-loop system is globally  exponentially stable. Such conditions can be easily  solved by linear programming. Finally, an example is  given to demonstrate the effectiveness of the proposed  method. 

Downloads

Download data is not yet available.

References

S. Liu and Z. Xiang, "Exponential L1 output tracking control for positive switched linear systems with time-varying delays," Nonlinear Analysis: Hybrid Systems, 2014, Vol. 11, pp. 118-128.

J. Zhang, Z. Hanand F. Zhu, "Finite-time control and L1-gain analysis for positive switched systems," Optimal Control Applications and Methods, 2015, Vol. 36, Issue. 4, pp. 550-565.

O. Mason and R. Shorten, "On linear copositive Lyapunov functions and the stability of switched positive linear systems," IEEE Transactions on Automatic Control, 2007, Vol. 52, Issue. 7, pp. 1346-1349.

B. Xia, J. Lian and X. H. Yuan, "Stability of switched positive descriptor systems with average dwell time switching," Journal of Shanghai Jiaotong University, 2015, Vol. 20, Issue. 2, pp. 177-184.

X. Liu and C. Dang, "Stability analysis of positive switched linear systems with delays", IEEE Transactions on Automatic Control, 2011, Vol. 56, Issue. 7, pp. 1684-1690.

M. Xiang and Z. Xiang, "Finite-time L1 control for positive switched linear systems with time-varying delay," Commun. Nonlinear Sci. Numer. Simul, 2013, Vol. 18, Issue. 11, pp. 3158-3166.

M. P. Aghababa and M. Borjkhani, "Chaotic fractional-order model for muscular blood vessel and its control via fractional control scheme," Complexity, 2015, Vol. 20, Issue. 2, pp. 37-46.

Baleanu, Dumitru, Guvenc and B. Ziya, "New Trends in Nanotechnology and Fractional Calculus Applications" 2014.

R. Hilfer, "Application of Fractional Calculus in Physics," World Scientific, 2000, Vol. 35, Issue. 12, i. [10]M. Ortigueira and T. Machado, "Special issue on fractional signal processing and applications," Signal Process, 2003, Vol. 83, Issue. 11, pp. 2285-2480. [11]T. T. Hartley, C. F. Lorenzo and H. K. Qammer, "Chaos in a fractional-order Chuas system," IEEE Trans Circ Syst I, 1995, Vol. 42, pp. 485-490. [12]J, Lu and G. Chen, "Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach," IEEE Transactions on Automatic Control, 2009, Vol. 54, Issue. 6, pp. 1294-1299.

J. Sabatier, M. Moze and C. Farges, "LMI stability conditions for fractional order systems," Computers and Mathematics with Applications 2010, Vol. 59, Issue. 5, pp. 1594-1609.

L. Chen, R. Wu, Y. He, et al, "Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties," Applied Mathematics and Computation, 2015, Vol. 257, Issue. C, pp. 274-284.

M. S. Tavazoei and M. Haeri, "A note on the stability of fractional order systems" Mathematics and Computers in Simulation, 2009, Vol. 79, Issue. 5, pp. 1566-1576.

C. Yin, Y. Cheng, S. Zhong, et al, "Fractional-order switching type control law design for adaptive sliding mode technique of 3D fractional-order nonlinear systems," Complexity, 2016, Vol. 21, Issue. 6, pp. 363-373.

Y. Chen, Y. Wei, H. Zhong, et al, "Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems," Nonlinear Dynamics, 2016, pp. 1-11.

S. Balochian, "Stabilization of autonomous linear time invariant fractional order derivative switched systems with different derivative in subsystems," Bulletin of the Polish Academy of Sciences Technical Sciences, 2014, Vol. 62, Isue. 3, pp. 495-503.

J. Shen and J. Lam, "Stability and Performance Analysis for Positive Fractional-Order Systems With Time-Varying Delays," emph{IEEE Transactions on Automatic Control}, 2016, Vol. 61, Issue. 9, pp. 2676-2681.

M. Busiowicz, "Robust stability of positive discrete-time linear systems of fractional order," Bulletin of the Polish Academy of Sciences Technical Sciences, 2010, Vol. 58, Issue. 4, pp. 567-572.

A. Babiarz, A. Legowski and M. Niezabitowski, "Controllability of positive discrete-time switched fractional order systems for fixed switching sequence," Lecture Notes in Artificial Intelligence, 2016, Vol. 9875, pp. 303-312.

X. Zhao, Y. Yin and X. Zheng, "State-dependent switching control of switched positive fractional-order systems," ISA Transactions, 2016, Vol. 62, pp. 103-108.

L. Liu, X. Cao, Z. Fu, et al, "Guaranteed cost finite-time control of fractional-order positive switched systems," Advances in Mathematical Physics, Vol. 2017, ID. 2695894.

Downloads

Published

2017-07-05

Issue

Vol. 5 No. 4 (2017): International Journal of Innovative Research in Computer Science & Technology(july)2017

Section

Articles

How to Cite

Global Exponential Stability and Stabilization of Fractional-Order Positive Switched Systems . (2017). International Journal of Innovative Research in Computer Science & Technology, 5(4), 333–338. Retrieved from https://acspublisher.com/journals/index.php/ijircst/article/view/13472