Robust exponential convergence of a class of linear delayed systems with bounded controllers and disturbances

Automatica ◽  
2006 ◽  
Vol 42 (11) ◽  
pp. 1863-1867 ◽  
Author(s):  
Said Oucheriah
Keyword(s):  
Exponential Convergence ◽  
Delayed Systems

Exponential Convergence of Delayed Dynamical Systems

2001 ◽  
Vol 13 (3) ◽  
pp. 621-635 ◽  
Author(s):  
Tianping Chen ◽  
Shun-ichi Amari
Keyword(s):  
Dynamical Systems ◽  
Exponential Convergence ◽  
Stability And Convergence ◽  
Delayed Systems ◽  
Mild Conditions

We discuss some delayed dynamical systems, investigating their stability and convergence. We prove that under mild conditions, these delayed systems are global exponential convergent.

Adaptive Variable Structure Control of Linear Delayed Systems

2004 ◽  
Vol 127 (4) ◽  
pp. 710-714 ◽  
Author(s):  
Said Oucheriah
Keyword(s):  
Exponential Convergence ◽  
Sliding Mode ◽  
External Disturbance ◽  
Variable Structure ◽  
Delay Systems ◽  
Delayed Systems ◽  
Reduced Order ◽  
Structure Control ◽  
Sliding Motion ◽  
Sliding Mode Dynamics

This brief deals with the stabilization of a class of time-delay systems subject to external disturbance vectors whose bounds are not known. A continuous adaptive variable structure controller is synthesized to guarantee that the motions of the sliding surface are uniformly exponentially convergent to a ball with any prespecified exponential convergence rate towards it. Furthermore, the reduced-order sliding mode dynamics as well as the deviation from ideal sliding motion are uniformly exponentially convergent to a ball whose radius is minimized and the exponential convergence towards it is maximized. The problem is formulated as an optimization problem with LMI constraints. Finally, an example is included to illustrate the results developed in this brief.

Noise Induced Switching in Delayed Systems

2012 ◽  
Author(s):  
Ira B. Schwartz ◽  
Thomas W. Carr ◽  
Lora Billings ◽  
Mark Dykman
Keyword(s):  
Delayed Systems

Enhanced Composite Nonlinear Control Technique using Adaptive Control for Nonlinear Delayed Systems

2020 ◽  
Vol 13 (3) ◽  
pp. 396-404
Author(s):  
Sonal Singh ◽  
Shubhi Purwar
Keyword(s):  
Adaptive Control ◽  
Actuator Saturation ◽  
Input Saturation ◽  
Chemical Reactor ◽  
Control Technique ◽  
Control Law ◽  
Nonlinear Feedback ◽  
Composite Nonlinear Feedback ◽  
Delayed Systems ◽  
Analysis Of Stability

Background and Introduction: The proposed control law is designed to provide fast reference tracking with minimal overshoot and to minimize the effect of unknown nonlinearities and external disturbances. Methods: In this work, an enhanced composite nonlinear feedback technique using adaptive control is developed for a nonlinear delayed system subjected to input saturation and exogenous disturbances. It ensures that the plant response is not affected by adverse effect of actuator saturation, unknown time delay and unknown nonlinearities/ disturbances. The analysis of stability is done by Lyapunov-Krasovskii functional that guarantees asymptotical stability. Results: The proposed control law is validated by its implementation on exothermic chemical reactor. MATLAB figures are provided to compare the results. Conclusion: The simulation results of the proposed controller are compared with the conventional composite nonlinear feedback control which illustrates the efficiency of the proposed controller.

scholarly journals A Razumikhin approach to exponential admissibility of switched descriptor delayed systems

2014 ◽  
Vol 38 (5-6) ◽  
pp. 1647-1659 ◽  
Author(s):  
Xiu Liu ◽  
Shouming Zhong ◽  
Xiuyong Ding
Keyword(s):  
Delayed Systems

scholarly journals A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Timon S. Gutleb
Keyword(s):  
Open Source ◽  
Spectral Method ◽  
Jacobi Polynomial ◽  
Numerical Experiments ◽  
Exponential Convergence ◽  
Analytic Solutions ◽  
Convolution Type ◽  
Volterra Equations ◽  
Polynomial Bases ◽  
Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

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