Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems

Automatica ◽  
2012 ◽  
Vol 48 (3) ◽  
pp. 499-504 ◽  
Author(s):  
Xianfu Zhang ◽  
Gang Feng ◽  
Yonghui Sun
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
State Feedback Control ◽  
Time Varying ◽  
Finite Time Stabilization

scholarly journals Finite-Time Stabilization of Switched Systems with Time-Varying Delay

2020 ◽  
pp. 24-31
Author(s):  
Mengxiao Deng ◽  
Yali Dong
Keyword(s):  
Feedback Control ◽  
Finite Time ◽  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Finite Time Stabilization ◽  
Varying Delay ◽  
Event Triggered

This paper studies the problem of finite-time stabilization of a class of switched linear time-varying delay systems. An event-triggered sampling mechanism and an event-triggered state feedback control are proposed. Based on Lyapunov-like function method, linear matrix inequality technique and averaged dwell time method, sufficient conditions for switched delay systems under event-triggered state feedback control are given to ensure the finite-time stabilization of the switched delay systems. Finally, a numerical example is given to verify the validity of the proposed results.

scholarly journals Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1146
Author(s):  
Călin-Adrian Popa ◽  
Eva Kaslik
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Fractional Order ◽  
Finite Time ◽  
State Feedback ◽  
Neutral Type ◽  
Leakage Delay ◽  
State Feedback Control ◽  
Time Varying ◽  
Control Scheme

This paper studies fractional-order neural networks with neutral-type delay, leakage delay, and time-varying delays. A sufficient condition which ensures the finite-time synchronization of these networks based on a state feedback control scheme is deduced using the generalized Gronwall–Bellman inequality. Then, a different state feedback control scheme is employed to realize the finite-time Mittag–Leffler synchronization of these networks by using the fractional-order extension of the Lyapunov direct method for Mittag–Leffler stability. Two numerical examples illustrate the feasibility and the effectiveness of the deduced sufficient criteria.

scholarly journals A Time-Varying Gain Design Method for State Feedback Control of Upper Triangular Nonlinear Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yanmin Yin
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Nonlinear Term ◽  
Design Method ◽  
State Feedback Control ◽  
Time Varying ◽  
Closed Loop System ◽  
Incremental Rate

In this paper, a time-varying gain design method is used to investigate the state feedback control problem of upper triangular nonlinear systems. Firstly, the nonlinear term recognizes an incremental rate relying on the unknown constant and the function with respect to time. Then, a time-varying gain design method is utilized to construct a state feedback controller. With the help of a suitable coordinate transformation and a Lyapunov function, one obtains that all the signals of the closed-loop system converge to zero. Finally, two numerical examples are presented to display the effectiveness of the time-varying gain design method.

scholarly journals Time-Varying Delayed H∞ Control Problem for Nonlinear Systems: A Finite Time Study Using Quadratic Convex Approach

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 713 ◽  
Author(s):  
Chanikan Emharuethai ◽  
Piyapong Niamsup ◽  
Raja Ramachandran ◽  
Wajaree Weera
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

In this manuscript, we consider the finite-time H ∞ control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a H ∞ controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time H ∞ state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.

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