Time-varying Control Lyapunov Function Design for Nonlinear Systems Defined on Manifolds

2018 ◽  
Author(s):  
Yoshiro Fukui
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Time Varying ◽  
Control Lyapunov Function ◽  
Function Design

An SOS-Based Control Lyapunov Function Design for Polynomial Fuzzy Control of Nonlinear Systems

2017 ◽  
Vol 25 (4) ◽  
pp. 775-787 ◽  
Author(s):  
Radian Furqon ◽  
Ying-Jen Chen ◽  
Motoyasu Tanaka ◽  
Kazuo Tanaka ◽  
Hua O. Wang
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Fuzzy Control ◽  
Control Lyapunov Function ◽  
Function Design

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.

scholarly journals Predefined-Time Antisynchronization of Two Different Chaotic Neural Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Lixiong Lin
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Time Stability ◽  
Stabilization Time ◽  
Control Lyapunov Function ◽  
Practical Advantage ◽  
Chaotic Neural Networks ◽  
Time Period ◽  
Function Design ◽  
Definition Of

This paper is concerned with antisynchronization in predefined time for two different chaotic neural networks. Firstly, a predefined-time stability theorem based on Lyapunov function is proposed. With the help of the definition of predefined time, it is convenient to establish a direct relationship between the tuning gain of the system and the fixed stabilization time. Then, the antisynchronization is achieved between two different chaotic neural networks via active control Lyapunov function design. The designed controller presents the practical advantage that the least upper bound for the settling time can be explicitly defined during the control design. With the help of the designed controller, the antisynchronization errors converge within a predefined-time period. Numerical simulations are presented in order to show the reliability of the proposed method.

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.

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