Stabilization of polynomial systems in ℝ3 via homogeneous feedback

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Hamadi Jerbi ◽  
Thouraya Kharrat ◽  
Fehmi Mabrouk
Keyword(s):  
Nonlinear Systems ◽  
Closed Loop ◽  
Polynomial Systems ◽  
Stabilization Problem ◽  
Odd Degree

Abstract In this paper, we study the stabilization problem of a class of polynomial systems of odd degree in dimension three. The constructed stabilizing feedback is homogeneous and guarantee the homogeneity of the closed loop system.mynotered In the end of the paper, we show the efficiency of such a study in the local stabilization of nonlinear systems affine in control.

scholarly journals Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Zaiyue Yang ◽  
C. W. Chan ◽  
Yiwen Wang
Keyword(s):  
Numerical Simulation ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Robust Stabilization ◽  
Control Coefficient ◽  
Control Performance ◽  
Stabilization Problem ◽  
Asymptotic Stabilization

This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.

scholarly journals State Feedback Control for Stochastic Feedforward Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Liang Liu ◽  
Ming Gao
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Asymptotically Stable ◽  
Stabilization Problem ◽  
Closed Loop System ◽  
Globally Asymptotically Stable ◽  
Feedforward Nonlinear Systems

This paper considers the state feedback stabilization problem for a class of stochastic feedforward nonlinear systems. By using the homogeneous domination approach, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability. A simulation example is provided to show the effectiveness of the designed controller.

scholarly journals A Fuzzy Approach to Robust Control of Stochastic Nonaffine Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Ting-Ting Gang ◽  
Jun Yang ◽  
Qing Gao ◽  
Yu Zhao ◽  
Jianbin Qiu
Keyword(s):  
Nonlinear Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Dynamic Feedback ◽  
Stabilization Problem ◽  
Fuzzy Models ◽  
Quadratic Lyapunov Functions ◽  
Affine Nonlinear Systems ◽  
Semiglobal Stabilization ◽  
Approximation Capability

This paper investigates the stabilization problem for a class of discrete-time stochastic non-affine nonlinear systems based on T-S fuzzy models. Based on the function approximation capability of a class of stochastic T-S fuzzy models, it is shown that the stabilization problem of a stochastic non-affine nonlinear system can be solved as a robust stabilization problem of the stochastic T-S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilization condition of the stochastic non-affine nonlinear systems is formulated in terms of linear matrix inequalities. A simulation example illustrating the effectiveness of the proposed approach is provided in the end.

scholarly journals The Adaptive Neural Control for a Class of High-Order Uncertain Stochastic Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Xiaoyan Qin
Keyword(s):  
Nonlinear Systems ◽  
Neural Control ◽  
Closed Loop ◽  
Control Method ◽  
High Order ◽  
Stochastic Nonlinear Systems ◽  
Closed Loop System ◽  
Adaptive Neural Control ◽  
Control Scheme ◽  
Approximation Capability

This paper studies the problem of the adaptive neural control for a class of high-order uncertain stochastic nonlinear systems. By using some techniques such as the backstepping recursive technique, Young’s inequality, and approximation capability, a novel adaptive neural control scheme is constructed. The proposed control method can guarantee that the signals of the closed-loop system are bounded in probability, and only one parameter needs to be updated online. One example is given to show the effectiveness of the proposed control method.

scholarly journals Finite frequency H∞control design for nonlinear systems

2021 ◽  
Vol 12 (1) ◽  
pp. 567
Author(s):  
Zineb Lahlou ◽  
Abderrahim EL-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Control Design ◽  
Loop Model ◽  
Finite Frequency

The work deals finite frequency H<sub>∞</sub> control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H<sub>∞</sub> lower can be by our method obtained developed where further comparison.

scholarly journals Global Finite-Time Stabilization Problem of Affine Nonlinear Systems with Unknown Functions

2021 ◽  
Author(s):  
Fujin Jia ◽  
Junwei Lu ◽  
Yong-Min Li ◽  
Fangyuan Li
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Control Algorithm ◽  
Lyapunov Analysis ◽  
Stabilization Problem ◽  
Analysis Method ◽  
Control Approach ◽  
Affine Nonlinear Systems ◽  
Simulation Results ◽  
Finite Time Stabilization

In this paper, the global finite-time stabilization (FTS) of nonlinear systems with unknown functions (UFs) is studied. Firstly, in order to deal with UFs, a Lemma is proposed to avoid the Assumptions of UFs. Secondly, based on this Lemma, the control algorithm designed by using backstepping has no partial derivative of virtual controllers, so it avoids the “differential explosion” problem of backstepping. Thirdly, by using Lyapunov analysis method, backstepping and FTS method, a global FTS control algorithm of nonlinear systems with UFs is proposed. Finally, the feasibility of developed control approach is illustrated by the simulation results of a manipulator.

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