Updating tk−1 is significant to Caputo fractional order switching systems: A reply to Hu’s comments

2022 ◽  
Vol 44 ◽  
pp. 101123
Cong Wu ◽  
Xinzhi Liu
2018 ◽  
Vol 7 (1) ◽  
pp. 85-96 ◽  
Seyed Hossein Nabavi ◽  
Saeed Balochian

Since switching systems are important in research and industry, the article is concerned about the stabilization of fractional order switching systems with the order of 1 < q < 2 and a time delay actuator. To this end, the so-called system was initially converted to a system with no delay using a trick, such that the impact of delay was considered in the state matrix of the system in form of a coefficient. In the following, the switching rule was obtained based on the variable structure control with the sliding section. The necessary stability condition for the fractional order switching system with the order of 1 < q < 2 and time delay actuator is presented and approved based on the convex analysis and linear matrix inequalities. Then, a Lyapunov function was introduced with its negative derivative. By defining the Lyapunov function, the system that can be chosen at any time by the switching rule would be stable. Finally, the simulation results were expressed to show the impact of the proposed method.

2013 ◽  
Vol 66 (5) ◽  
pp. 585-596 ◽  
S. Hassan HosseinNia ◽  
Inés Tejado ◽  
Blas M. Vinagre

2012 ◽  
Vol 6 (3) ◽  
pp. 445-451 ◽  
S. Hassan Hosseinnia ◽  
Inés Tejado ◽  
Blas M. Vinagre ◽  
Dominik Sierociuk

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