Novel Fixed-Time Stability Criteria for Discontinuous Nonautonomous Systems: Lyapunov Method With Indefinite Derivative

This paper studies the fixed-time stability problem for positive nonlinear systems defined by cooperative vector fields. A criterion is derived to ensure fixed-time stabilization of the positive nonlinear systems using Lyapunov method. In addition, a sufficient condition is also presented for fixed-time stability of switched positive nonlinear systems under arbitrary switching. Simulation examples are provided to demonstrate the obtained results.

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Improved fixed‐time stability results and application to synchronization of discontinuous neural networks with state‐dependent switching

International Journal of Robust and Nonlinear Control ◽

10.1002/rnc.5566 ◽

2021 ◽

Author(s):

Abdujelil Abdurahman ◽

Haijun Jiang ◽

Cheng Hu

Keyword(s):

Neural Networks ◽

Fixed Time ◽

Time Stability ◽

State Dependent ◽

Discontinuous Neural Networks ◽

Stability Results

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Fixed time stability of a class of chaotic systems with disturbances by using sliding mode control

ISA Transactions ◽

10.1016/j.isatra.2021.02.012 ◽

2021 ◽

Author(s):

Haipeng Su ◽

Runzi Luo ◽

Jiaojiao Fu ◽

Meichun Huang

Keyword(s):

Sliding Mode Control ◽

Chaotic Systems ◽

Sliding Mode ◽

Fixed Time ◽

Time Stability ◽

Mode Control

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Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control

Mathematical Problems in Engineering ◽

10.1155/2017/4903963 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Maoxing Liu ◽

Jie Wu ◽

Yong-zheng Sun

Keyword(s):

Stability Analysis ◽

Permanent Magnet ◽

Initial Conditions ◽

Lyapunov Stability Theory ◽

Fixed Time ◽

Stability Control ◽

Time Stability ◽

Permanent Magnet Synchronous Motors ◽

Synchronous Motors ◽

Comparison Results

We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.

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Adaptive fuzzy fault‐tolerant control for non‐linear systems under actuator and sensor faults: the practical fixed‐time stability

IET Control Theory and Applications ◽

10.1049/iet-cta.2020.0689 ◽

2020 ◽

Vol 14 (19) ◽

pp. 3291-3300

Author(s):

Yekai Yang ◽

Yugang Niu ◽

Zhina Zhang

Keyword(s):

Linear Systems ◽

Fault Tolerant ◽

Fault Tolerant Control ◽

Fixed Time ◽

Sensor Faults ◽

Time Stability ◽

Adaptive Fuzzy ◽

Non Linear ◽

Non Linear Systems

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Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

Neural Computation ◽

10.1162/neco.2009.08-08-840 ◽

2009 ◽

Vol 21 (12) ◽

pp. 3444-3459 ◽

Cited By ~ 3

Author(s):

Wei Lin

Keyword(s):

Neural Networks ◽

Periodic Solution ◽

Lyapunov Method ◽

Autonomous Systems ◽

Neural Systems ◽

Stability Criteria ◽

Volterra System ◽

Numerical Examples ◽

The Stability ◽

Special Case

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the [Formula: see text]-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.

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Fixed time synchronization of a class of chaotic systems based via the saturation control

Revista Mexicana de Física ◽

10.31349/revmexfis.67.041401 ◽

2021 ◽

Vol 67 (4 Jul-Aug) ◽

pp. 041401

Author(s):

Jiaojiao Fu ◽

Runzi Luo ◽

Meichun Huang ◽

Haipeng Su

Keyword(s):

Upper Bound ◽

Chaotic Systems ◽

Time Synchronization ◽

Fixed Time ◽

Stability Theorem ◽

Backstepping Method ◽

Time Stability ◽

Saturation Control ◽

New Chaotic System ◽

Upper Bound Estimate

In this paper, we discuss the fixed time synchronization of a class of chaotic systems based on the backstepping control with disturbances. A new and important fixed time stability theorem is presented. The upper bound estimate formulas of the settling time are also given which are different from the existing results in the literature. Based on the new fixed time stability theorem, a novel saturation controller for the fixed time synchronization a class of chaotic systems is proposed via the backstepping method. Finally, the new chaotic system is taken as an example to illustrate the applicability of the obtained theory.

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