scholarly journals A Strict Control Lyapunov Function for a Diffusion Equation With Time-Varying Distributed Coefficients

2013 ◽  
Vol 58 (2) ◽  
pp. 290-303 ◽  
Author(s):  
Federico Bribiesca Argomedo ◽  
Christophe Prieur ◽  
Emmanuel Witrant ◽  
Sylvain Bremond
Keyword(s):  
Lyapunov Function ◽  
Diffusion Equation ◽  
Time Varying ◽  
Control Lyapunov Function ◽  
Strict Control

Control of Nonlinear Systems in Normal Form by Complementary Lyapunov Functions

2017 ◽  
Author(s):  
Andy Zelenak ◽  
Benito Fernández ◽  
Mitch Pryor
Keyword(s):  
Lyapunov Function ◽  
Normal Form ◽  
Lyapunov Functions ◽  
General Type ◽  
Order System ◽  
Time Varying ◽  
Control Lyapunov Function ◽  
New Approach ◽  
Complementary Function ◽  
Siso Systems

If a Lyapunov function is known, a dynamic system can be stabilized. However, the search for a Lyapunov function is often challenging. This paper takes a new approach to avoid such a search; it assumes a basic Control Lyapunov Function [CLF] then seeks to numerically diminish the value of the Lyapunov function. If a singularity arises during calculations with the default CLF, a complementary function is used. The complementary function eliminates a common cause of singularities with the default CLF. While many other algorithms from the literature use switched or time-varying CLF’s, the presented method is unique in that the CLF’s do not require prior calculation and the technique applies globally. The method is proven and demonstrated for SISO systems in normal form and then demonstrated on a higher-order system of a more general type.

Multilayer minimum projection method for nonsmooth strict control Lyapunov function design

2010 ◽  
Vol 59 (9) ◽  
pp. 563-570 ◽  
Author(s):  
Hisakazu Nakamura ◽  
Yoshiro Fukui ◽  
Nami Nakamura ◽  
Hirokazu Nishitani
Keyword(s):  
Lyapunov Function ◽  
Projection Method ◽  
Control Lyapunov Function ◽  
Strict Control ◽  
Function Design

Cooperative Networked Control Based on a Time-Varying Lyapunov Function

2021 ◽  
Vol 32 (3) ◽  
pp. 533-542
Author(s):  
Arturo M. Flores ◽  
Lucas N. Egidio ◽  
Grace S. Deaecto
Keyword(s):  
Lyapunov Function ◽  
Networked Control ◽  
Time Varying

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

2021 ◽  
pp. 107754632098598
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Multiple Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Common Lyapunov Function ◽  
Suggested Approach ◽  
Aggregation Techniques

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.

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