Comments on “Lyapunov and external stability of Caputo fractional order switching systems”

2021 ◽  
Vol 40 ◽  
pp. 101016
Author(s):  
Jianbing Hu
Keyword(s):  
Fractional Order ◽  
Switching Systems ◽  
External Stability

The Stability of a Class of Fractional Order Switching System with Time-Delay Actuator

2018 ◽  
Vol 7 (1) ◽  
pp. 85-96 ◽  
Author(s):  
Seyed Hossein Nabavi ◽  
Saeed Balochian
Keyword(s):  
Time Delay ◽  
Lyapunov Function ◽  
Fractional Order ◽  
Variable Structure ◽  
Linear Matrix ◽  
Switching Systems ◽  
Switching System ◽  
State Matrix ◽  
Switching Rule ◽  
The Impact

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.

scholarly journals Stability of fractional order switching systems

2013 ◽  
Vol 66 (5) ◽  
pp. 585-596 ◽  
Author(s):  
S. Hassan HosseinNia ◽  
Inés Tejado ◽  
Blas M. Vinagre
Keyword(s):  
Fractional Order ◽  
Switching Systems

Boolean-based fractional order SMC for switching systems: application to a DC-DC buck converter

2012 ◽  
Vol 6 (3) ◽  
pp. 445-451 ◽  
Author(s):  
S. Hassan Hosseinnia ◽  
Inés Tejado ◽  
Blas M. Vinagre ◽  
Dominik Sierociuk
Keyword(s):  
Fractional Order ◽  
Buck Converter ◽  
Switching Systems

scholarly journals External stability and $H_{\infty }$ control of switching systems with delay and impulse

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jiaojiao Ren ◽  
Cong Wu
Keyword(s):  
Switching Systems ◽  
Time Varying ◽  
Internal Dynamics ◽  
Switching Law ◽  
External Stability ◽  
Time Varying Delay ◽  
Norm Constraint ◽  
Varying Delay ◽  
Maximum Minimum ◽  
Inequality Relation

AbstractIn this paper, we investigate the external stability and $H_{\infty }$ H ∞ control of switching systems with time-varying delay and impulse. First of all, a modified two-direction inequality (relation) between the switching numbers and the maximum, minimum dwell time is proposed. This new inequality is applied to proving the external stability of switching systems with delay and impulse consisting of subsystems with Hurwitz stable matrices of internal dynamics. By using this new inequality, a normal $L_{2}$ L 2 norm constraint is derived rather than weighted $L_{2}$ L 2 norm constraint. In addition, by a realizable switching law, the obtained result is extended to the switching systems comprised of subsystems with both Hurwitz stable and unstable matrices of internal dynamics. The results are finally applied to $H_{\infty }$ H ∞ control and illustrated by a numerical example.

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