scholarly journals Consistent Discretization of Finite-Time and Fixed-Time Stable Systems

2019 ◽  
Vol 57 (1) ◽  
pp. 78-103 ◽  
Author(s):  
Andrey Polyakov ◽  
Denis Efimov ◽  
Bernard Brogliato
Keyword(s):  
Finite Time ◽  
Fixed Time

Fixed-time fractional-order sliding mode control for nonlinear power systems

2020 ◽  
Vol 26 (17-18) ◽  
pp. 1425-1434 ◽  
Author(s):  
Sunhua Huang ◽  
Jie Wang
Keyword(s):  
Sliding Mode Control ◽  
Power System ◽  
Fractional Order ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Fixed Time ◽  
Sliding Mode Controller ◽  
Mode Control ◽  
Time Control

In this study, a fractional-order sliding mode controller is effectively proposed to stabilize a nonlinear power system in a fixed time. State trajectories of a nonlinear power system show nonlinear behaviors on the angle and frequency of the generator, phase angle, and magnitude of the load voltage, which would seriously affect the safe and stable operation of the power grid. Therefore, fractional calculus is applied to design a fractional-order sliding mode controller which can effectively suppress the inherent chattering phenomenon in sliding mode control to make the nonlinear power system converge to the equilibrium point in a fixed time based on the fixed-time stability theory. Compared with the finite-time control method, the convergence time of the proposed fixed-time fractional-order sliding mode controller is not dependent on the initial conditions and can be exactly evaluated, thus overcoming the shortcomings of the finite-time control method. Finally, superior performances of the fractional-order sliding mode controller are effectively verified by comparing with the existing finite-time control methods and integral order sliding mode control through numerical simulations.

scholarly journals On Implicit Finite- Time and Fixed- Time ISS Lyapunov Functions

2018 ◽  
Author(s):  
F. Lopez-Ramirez ◽  
D. Efimov ◽  
A. Polyakov ◽  
W. Perruquettil
Keyword(s):  
Finite Time ◽  
Lyapunov Functions ◽  
Fixed Time
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