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

scholarly journals Algunos errores en el uso de funciones de Lyapunov para control de estructura variable

2021 ◽  
Vol 8 (16) ◽  
pp. 11-17
Author(s):  
David Ismael Vázquez-Dueñas ◽  
Jorge Luis Álvarez-Urias
Keyword(s):  
Lyapunov Function ◽  
Finite Time ◽  
Lyapunov Functions ◽  
Fixed Time ◽  
Second Order ◽  
Function Approach ◽  
Set Design ◽  
Lmi Approach ◽  
Finite Time Stabilization

Este trabajo discute errores encontrados en el uso de funciones de Lyapunov propuestas en resultados recientes de control de estructura variable: en diseños continuos con convergencia en tiempo finito (``Continuous finite-time stabilization of the translational and rotational double integrators'' por Bhat y Bernstein, 1998), basados en funciones implícitas de Lyapunov (``Finite-time and fixed-time stabilization: implicit Lyapunov function approach'' por Polyakov et al, 2015), y basados en funciones de Lyapunov discontinuas por partes (``An LMI approach for second-order sliding set design using piecewise Lyapunov functions'' Tapia et al, 2017).

Introduction

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
Lyapunov Functions ◽  
Large Scale ◽  
Interconnected Systems ◽  
Large Scale Systems ◽  
Vector Lyapunov Functions ◽  
Finite Time Stabilization ◽  
And Control ◽  
Interconnected Dynamical Systems

This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, with an emphasis on vector Lyapunov function methods and vector dissipativity theory. It examines large-scale continuous-time interconnected dynamical systems and describes thermodynamic modeling of large-scale interconnected systems, along with the use of vector Lyapunov functions to control large-scale dynamical systems. It also discusses finite-time stabilization of large-scale systems via control vector Lyapunov functions, coordination control for multiagent interconnected systems, large-scale impulsive dynamical systems, finite-time stabilization of large-scale impulsive dynamical systems, and hybrid decentralized maximum entropy control for large-scale systems. This chapter provides a brief introduction to large-scale interconnected dynamical systems as well as an overview of the book's structure.

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.

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