scholarly journals Exponential Stability for the Schlögl System by Pyragas Feedback

2020 ◽  
Vol 48 (4) ◽  
pp. 769-790
Author(s):  
Martin Gugat ◽  
Mariano Mateos ◽  
Fredi Tröltzsch
Keyword(s):  
Exponential Stability ◽  
Closed Loop ◽  
Reaction Diffusion ◽  
Distributed Feedback ◽  
Classical Type ◽  
Closed Loop System ◽  
Cubic Nonlinearity ◽  
Nonlinear Reaction ◽  
Periodic State ◽  
Feedback Laws

AbstractThe Schlögl system is governed by a nonlinear reaction-diffusion partial differential equation with a cubic nonlinearity. In this paper, feedback laws of Pyragas-type are presented that stabilize the system in a periodic state with a given period and given boundary traces. We consider the system both with boundary feedback laws of Pyragas type and distributed feedback laws of Pyragas and classical type. Stabilization to periodic orbits is important for medical applications that concern Parkinson’s disease. The exponential stability of the closed loop system with respect to the L2-norm is proved. Numerical examples are provided.

scholarly journals Stabilization of Variable Coefficients Euler-Bernoulli Beam with Viscous Damping under a Force Control in Rotation and Velocity Rotation

2017 ◽  
Vol 9 (6) ◽  
pp. 1
Author(s):  
Bomisso G. Jean Marc ◽  
Tour\'{e} K. Augustin ◽  
Yoro Gozo
Keyword(s):  
Exponential Stability ◽  
Force Control ◽  
Riesz Basis ◽  
Closed Loop ◽  
Variable Coefficients ◽  
Viscous Damping ◽  
Closed Loop System ◽  
Bernoulli Beam ◽  
Spectral System ◽  
Euler Bernoulli Beam

This paper investigates the problem of exponential stability for a damped Euler-Bernoulli beam with variable coefficients clamped at one end and subjected to a force control in rotation and velocity rotation. We adopt the Riesz basis approach for show that the closed-loop system is a Riesz spectral system. Therefore, the exponential stability and the spectrum-determined growth condition are obtained.

scholarly journals Exponential Stability of the Monotubular Heat Exchanger Equation with Time Delay in Boundary Observation

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Xue-Lian Jin ◽  
Yang Zhang ◽  
Fu Zheng ◽  
Bao-zhu Guo
Keyword(s):  
Heat Exchanger ◽  
Time Delay ◽  
Exponential Stability ◽  
Closed Loop ◽  
Abstract Cauchy Problem ◽  
Loop System ◽  
Physical Parameters ◽  
Closed Loop System ◽  
Close Loop System ◽  
Resolvent Estimates

The exponential stability of the monotubular heat exchanger equation with boundary observation possessing a time delay and inner control was investigated. Firstly, the close-loop system was translated into an abstract Cauchy problem in the suitable state space. A uniformly bounded C0-semigroup generated by the close-loop system, which implies that the unique solution of the system exists, was shown. Secondly, the spectrum configuration of the closed-loop system was analyzed and the eventual differentiability and the eventual compactness of the semigroup were shown by the resolvent estimates on some resolvent sets. This implies that the spectrum-determined growth assumption holds. Finally, a sufficient condition, which is related to the physical parameters in the system and is independent of the time delay, of the exponential stability of the closed-loop system was given.

scholarly journals Sector stability criteria for a nonlinear axial motion string system

2021 ◽  
Author(s):  
Rui Wu ◽  
Yi Cheng ◽  
Donal O'Regan
Keyword(s):  
Exponential Stability ◽  
Closed Loop ◽  
Semigroup Theory ◽  
Nonlinear Partial Differential Equation ◽  
Loop System ◽  
Closed Loop System ◽  
Axially Moving ◽  
The Right ◽  
Nonlinear Semigroup Theory ◽  
Control Criterion

The paper investigates the exponential stability criterion for an axially moving string system driven by a nonlinear partial differential equation with nonlinear boundary feedback.The control criterion based on a sector condition contains a large class of nonlinearities, which is a negative feedback of the velocity at the right boundary of the moving string. By invoking nonlinear semigroup theory, the well-posedness result of the closed-loop system is verified under the sector criteria. Furthermore, a novel energy like function is constructed to establish the exponential stability of the closed-loop system by using a integral-type multiplier method and the generalized Gronwall-type integral inequality.

scholarly journals Stabilization of a certain class of fuzzy control systems with uncertainties

2017 ◽  
Vol 27 (3) ◽  
pp. 453-481
Author(s):  
Nizar Hadj Taieb ◽  
Mohamed Ali Hammami ◽  
François Delmotte
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Control Systems ◽  
Fuzzy Systems ◽  
Closed Loop ◽  
Exponential Convergence ◽  
Closed Loop System ◽  
Quadratic Lyapunov Function ◽  
Integrable Functions ◽  
Takagi Sugeno

AbstractIn this paper, we investigate the global uniform practical exponential stability for a class of uncertain Takagi-Sugeno fuzzy systems. The uncertainties are supposed uniformly to be bounded by some known integrable functions to obtain an exponential convergence toward a neighborhood of the origin. Therefore, we use common quadratic Lyapunov function (CQLF) and parallel distributed compensation (PDC) controller techniques to show the global uniform practical exponential stability of the closed-loop system. Numeric simulations are given to validate the proposed approach.

Finite-time boundary stabilization of the reaction-diffusion system with switching time-delay input

2021 ◽  
pp. 014233122110325
Author(s):  
Najmeh Ghaderi ◽  
Mohammad Keyanpour ◽  
Hamed Mojallali
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Closed Loop ◽  
Switching Time ◽  
Reaction Diffusion ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Time Control ◽  
Time Simulation ◽  
Switching Controller

The paper is devoted to the study of boundary finite-time control for a reaction-diffusion (RD) system with switching time-delayed input. The RD system with switching time-delay input is converted to a switching system of RD equation cascaded with a transport equation with non-delay boundary input. Next, a novel switching controller is designed for the cascaded RD-transport system based on the backstepping technique, and this causes the closed-loop system to be convergence in a finite-time. Simulation results are provided to exhibit the effectiveness of the proposed method.

scholarly journals Boundary Stabilization of Heat Equation with Multi-Point Heat Source

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 834
Author(s):  
Qing-Qing Hu ◽  
Feng-Fei Jin ◽  
Bao-Qiang Yan
Keyword(s):  
Heat Source ◽  
Heat Equation ◽  
Exponential Stability ◽  
Output Feedback ◽  
Closed Loop ◽  
Feedback Controller ◽  
Loop System ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Point Heat Source

In this paper, we consider boundary stabilization problem of heat equation with multi-point heat source. Firstly, a state feedback controller is designed mainly by backstepping approach. Under the designed state controller, the exponential stability of closed-loop system is guaranteed. Then, an observer-based output feedback controller is proposed. We prove the exponential stability of resulting closed-loop system using operator semigroup theory. Finally, the designed state and output feedback controllers are effective via some numerical simulations.

scholarly journals Exponential stability of axially moving Kirchhoff-beam systems with nonlinear boundary damping and disturbance

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yi Cheng ◽  
Zhihui Dong ◽  
Donal O' Regan
Keyword(s):  
Exponential Stability ◽  
Closed Loop ◽  
Initial Conditions ◽  
Galerkin Approximation ◽  
Nonlinear Damping ◽  
Loop System ◽  
Direct Lyapunov Method ◽  
Closed Loop System ◽  
Uniqueness Of Solutions ◽  
Axially Moving

<p style='text-indent:20px;'>This paper examines the stabilization problem of the axially moving Kirchhoff beam. Under the nonlinear damping criterion established by the slope-restricted condition, the existence and uniqueness of solutions of the closed-loop system equipped with nonlinear time-delay disturbance at the boundary is investigated via the Faedo-Galerkin approximation method. Furthermore, the solution is continuously dependent on initial conditions. Then the exponential stability of the closed-loop system is established by the direct Lyapunov method, where a novel energy function is constructed.</p>

Study of Complex Networked Control System Exponential Stability

2014 ◽  
Vol 926-930 ◽  
pp. 2106-2109
Author(s):  
Yue Pan
Keyword(s):  
Control System ◽  
Exponential Stability ◽  
Dynamic System ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Integrated Model ◽  
Networked Control System ◽  
Data Loss ◽  
Closed Loop System ◽  
Necessary And Sufficient

An integrated model considering all complex factors was provided. Combined with data Loss Tolerance and build an asynchronous dynamic system consisting observer and controller in the closed-loop system. The necessary and sufficient conditions to make the system index stable were analyzed.

scholarly journals Exponential stabilization of a linear Korteweg-de Vries equation with input saturation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ahmat Mahamat Taboye ◽  
Mohamed Laabissi
Keyword(s):  
Exponential Stability ◽  
Closed Loop ◽  
Vries Equation ◽  
Input Saturation ◽  
Loop System ◽  
Exponential Stabilization ◽  
Closed Loop System ◽  
De Vries ◽  
Exponentially Stable ◽  
Well Posed

<p style='text-indent:20px;'>This article deals with the issue of the exponential stability of a linear Korteweg-de Vries equation with input saturation. It is proved that the system is well-posed and the origin is exponentially stable for the closed loop system, by using the classical argument used in this kind of problems.</p>

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