Finite-time stabilization of stochastic coupled systems on networks by feedback control and its application

2019 ◽  
Vol 37 (3) ◽  
pp. 814-830
Author(s):  
Yongbao Wu ◽  
Wenxue Li ◽  
Jiqiang Feng
Keyword(s):  
Finite Time ◽  
Coupled Oscillators ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Convergence Time ◽  
Practical Application ◽  
Finite Time Stability ◽  
Finite Time Stabilization ◽  
Theoretical Results

Abstract In this paper, the finite-time stabilization of stochastic coupled systems on networks (SCSNs) is studied. Different from previous research methods, the method used in this paper combines Lyapunov method with graph theory, and some novel sufficient conditions are obtained to ensure finite-time stability for SCSNs. Meanwhile, the convergence time is closely related to topological structure in networks. As a practical application in physics, we address a concrete finite-time stabilization problem of stochastic coupled oscillators through our main results. In addition, a numerical example is presented to illustrate the effectiveness and feasibility of the theoretical results.

scholarly journals Finite-Time Robust Stabilization for Stochastic Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Weixiong Jin ◽  
Xiaoyang Liu ◽  
Xiangjun Zhao ◽  
Nan Jiang ◽  
Zhengxin Wang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Nonlinear Systems ◽  
Stochastic Neural Networks ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Stabilization

This paper is concerned with the finite-time stabilization for a class of stochastic neural networks (SNNs) with noise perturbations. The purpose of the addressed problem is to design a nonlinear stabilizator which can stabilize the states of neural networks in finite time. Compared with the previous references, a continuous stabilizator is designed to realize such stabilization objective. Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are established for ensuring the finite-time stability of the dynamics of SNNs in probability. Then, the gain parameters of the finite-time controller could be obtained by solving a linear matrix inequality and the robust finite-time stabilization could also be guaranteed for SNNs with uncertain parameters. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.

Finite-time stability of spring-mass system with unilateral impact constraints and frictions

2020 ◽  
Vol 34 (30) ◽  
pp. 2050341
Author(s):  
Ruiyang Qiu ◽  
Ruihai Li
Keyword(s):  
Finite Time ◽  
Sliding Friction ◽  
Sufficient Conditions ◽  
Step Function ◽  
Time Varying ◽  
Time Stability ◽  
Mass System ◽  
Finite Time Stability ◽  
Air Resistance ◽  
Theoretical Results

In this paper, a spring-mass system with impacts and frictions is formulated by the impulsive differential system. An energy-like Lyapunov function and an auxiliary step function are constructed to analyze the finite-time stability of such impact system with a time-varying external force and sliding friction as well as air resistance. We establish the sufficient conditions of finite-time stability for three cases of the spring-mass system, and present numerical simulations for each case to verify the validity of the theoretical results.

scholarly journals Finite-time stabilization of switched nonlinear singular systems with asynchronous switching

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Wang ◽  
Xingtao Wang
Keyword(s):  
Finite Time ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Original System ◽  
Linear Matrix ◽  
Finite Time Stability ◽  
Nonlinear Singular Systems ◽  
Time Period ◽  
Finite Time Stabilization

AbstractThis paper is concerned with the finite-time stabilization of a class of switched nonlinear singular systems under asynchronous control. Asynchronism here refers to the delays in switching between the controller and the subsystem. First, the dynamic decomposition technique is used to prove that such a switched singular system is regular and impulse-free. Secondly, based on the state solutions of the closed-loop system in the matched time period and the mismatched time period of the system instead of constructing a Lyapunov function, the sufficient conditions for the finite-time stability of the asynchronous switched singular system are given, there is no limit to the stability of subsystems. Then, the mode-dependent state feedback controller that makes the original system stable is derived in the form of strict linear matrix inequalities. Finally, numerical examples are given to verify the feasibility and validity of the results.

scholarly journals Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Minsong Zhang
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Time Stability ◽  
Quadratic Systems ◽  
Finite Time Stability ◽  
Jump Time ◽  
Stability And Stabilization ◽  
Finite Time Stabilization

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Periodically intermittent control for synchronized stationary distribution and synchronization of memristor-based stochastic coupled systems

2019 ◽  
Vol 41 (14) ◽  
pp. 4142-4156
Author(s):  
Yan Liu ◽  
Wenxue Li ◽  
Kaiwen Feng ◽  
Huihui Song
Keyword(s):  
Stationary Distribution ◽  
Control Strategy ◽  
Coupled Oscillators ◽  
Lyapunov Method ◽  
Coupled Systems ◽  
Intermittent Control ◽  
Periodically Intermittent Control ◽  
A New Technique ◽  
First Time ◽  
Theoretical Results

This article is concerned with inner synchronized stationary distribution for memristor-based stochastic coupled systems for the first time. It is worth mentioning that periodically intermittent control that serves as a new technique is introduced into the investigation of synchronized stationary distribution. Based on the graph theory, the Lyapunov method and periodically intermittent control strategy, two main theorems that guarantee the existence of a synchronized stationary distribution are obtained, whose results illustrate that the existing region of synchronized stationary distribution depends on the control rate, coupled strength and so on. On the other hand, exponential synchronization is also taken into consideration and a theorem is presented. In addition, as applications, memristor-based stochastic coupled oscillators and stochastic coupled Chua’s circuits are presented to verify the practicability of theoretical results. Finally, two simulation examples are given to demonstrate the effectiveness and feasibility of theoretical results.

scholarly journals Finite-Time Stabilization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delay

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Ge Li ◽  
Yaqiong Li ◽  
Zhaohui Yuan
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Time Varying ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Finite Time Stabilization ◽  
Varying Delay

In this paper, the finite-time stabilization problem for memristive Cohen-Grossberg neural networks with time-varying delay is discussed. By using the novel fixed point theory of set-valued maps, we establish the existence theorem of equilibrium point. In order to realize the finite-time stabilization, two different kinds of discontinuous state feedback controllers whether including time-varying delay are designed. Based on the extended Filippov framework and two different kinds of methods whether using finite-time stability theory, some novel sufficient conditions and the upper bound of the settling time for finite-time stabilization are proposed. Finally, two numerical examples are given to demonstrate the validity of theoretical results.

scholarly journals Finite-time generalized synchronization of nonidentical delayed chaotic systems

2016 ◽  
Vol 21 (3) ◽  
pp. 306-324 ◽  
Author(s):  
Haibo Bao ◽  
Jinde Cao
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Convergence Time ◽  
Generalized Synchronization ◽  
Delayed Systems ◽  
Finite Time Stability ◽  
Control Techniques ◽  
Nonlinear Control Theory ◽  
Response Systems

This paper deals with the finite-time generalized synchronization (GS) problem of drive-response systems. The main purpose of this paper is to design suitable controllers to force the drive-response system realize GS in a finite time. Based on the finite-time stability theory and nonlinear control theory, sufficient conditions are derived that guarantee finite-time GS. This paper extends some basic results from generalized synchronization to delayed systems. Because finite-time GS means the optimality in convergence time and has better robustness, the results in this paper are important. Numerical examples are given to show the effectiveness of the proposed control techniques.

scholarly journals Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255797
Author(s):  
Baozeng Fu ◽  
Qingzhi Wang ◽  
Ping Li
Keyword(s):  
Output Feedback ◽  
Finite Time ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Hamilton Function ◽  
Pch System ◽  
Inequality Technique ◽  
Finite Time Stabilization ◽  
Theoretical Results

The finite-time stabilization and finite-time H∞ control problems of Port-controlled Hamiltonian (PCH) systems with disturbances and input saturation (IS) are studied in this paper. First, by designing an appropriate output feedback, a strictly dissipative PCH system is obtained and finite-time stabilization result for nominal system is given. Second, with the help of the Hamilton function method and truncation inequality technique, a novel output feedback controller is developed to make the PCH system finite-time stable when IS occurs. Further, a finite-time H∞ controller is designed to attenuate disturbances for PCH systems with IS, and sufficient conditions are presented. Finally, a numerical example and a circuit example are given to reveal the feasibility of the obtained theoretical results.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

scholarly journals Finite-Time Adaptive Fuzzy Control for Nonlinear Systems with Unknown Backlash-Like Hysteresis

2021 ◽  
Author(s):  
Shuzhen Diao ◽  
Wei Sun ◽  
Le Wang ◽  
Jing Wu
Keyword(s):  
Fuzzy Control ◽  
Finite Time ◽  
Fuzzy Systems ◽  
Tracking Error ◽  
Adaptive Fuzzy Control ◽  
Finite Time Stability ◽  
Adaptive Fuzzy ◽  
Intermediate Variable ◽  
Control Scheme ◽  
Theoretical Results

AbstractThis study considers the tracking control problem of the nonstrict-feedback nonlinear system with unknown backlash-like hysteresis, and a finite-time adaptive fuzzy control scheme is developed to address this problem. More precisely, the fuzzy systems are employed to approximate the unknown nonlinearities, and the design difficulties caused by the nonlower triangular structure are also overcome by using the property of fuzzy systems. Besides, the effect of unknown hysteresis input is compensated by approximating an intermediate variable. With the aid of finite-time stability theory, the proposed control algorithm could guarantee that the tracking error converges to a smaller region. Finally, a simulation example is provided to further verify the above theoretical results.

Sign in / Sign up

Export Citation Format

Share Document