A generalized Barbalat lemma based on a persistently exciting condition

2014 ◽  
Author(s):  
Ti-Chung Lee
Keyword(s):  
Barbalat Lemma

Stabilization for a class of delayed switched inertial neural networks via non-reduced order method

2021 ◽  
pp. 014233122098594
Author(s):  
Xuan Chen ◽  
Dongyun Lin
Keyword(s):  
Neural Networks ◽  
Comparative Research ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Global Stabilization ◽  
Order Method ◽  
Reduced Order ◽  
Global Asymptotic Stabilization ◽  
Inertial Neural Networks ◽  
Barbalat Lemma

This paper tackles the issue of global stabilization for a class of delayed switched inertial neural networks (SINN). Distinct from the frequently employed reduced-order technique, this paper studies SINN directly through non-reduced order method. By constructing a novel Lyapunov functional and using Barbalat Lemma, sufficient conditions for the global asymptotic stabilization issue and global exponential stabilization issue of the considered SINN are established. Numerical simulations further confirm the feasibility of the main results. The comparative research shows that global stabilization results of this paper complement and improve some existing work.

Discussion on Barbalat Lemma extensions for conformable fractional integrals

2017 ◽  
Vol 92 (2) ◽  
pp. 234-241 ◽  
Author(s):  
A. Souahi ◽  
O. Naifar ◽  
A. Ben Makhlouf ◽  
M. A. Hammami
Keyword(s):  
Fractional Integrals ◽  
Barbalat Lemma

scholarly journals Synchronization of Coupled Networks with Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Yi Zuo ◽  
Xinsong Yang
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Nonlinear Perturbations ◽  
Coupled Networks ◽  
Barbalat Lemma ◽  
Asymptotic Synchronization ◽  
Theoretical Results

Asymptotic synchronization for a class of coupled networks with nondelayed and delayed couplings is investigated. A distinct feature of the network is that all the dynamical nodes are affected by uncertain nonlinear nonidentical perturbations. In order to synchronize the network onto a given isolate trajectory, a novel adaptive controller is designed to overcome the effects of the nonidentical uncertain nonlinear perturbations. The designed controller has better robustness than classical adaptive controller, since it can realize the synchronization goal whether the nodes have these perturbations or not. Based on the Lyapunov stability theory and the Barbalat lemma, sufficient conditions guaranteeing the asymptotic synchronization of the coupled network are derived. Two examples with numerical simulations are given to illustrate the effectiveness of the theoretical results. Simulations also demonstrate that our adaptive controller has better robustness than existing ones.

On fractional extensions of Barbalat Lemma

2015 ◽  
Vol 84 ◽  
pp. 7-12 ◽  
Author(s):  
Javier A. Gallegos ◽  
Manuel A. Duarte-Mermoud ◽  
Norelys Aguila-Camacho ◽  
Rafael Castro-Linares
Keyword(s):  
Barbalat Lemma

H∞ Control of Fuzzy Neutral Systems under Sampled-Data Control

2010 ◽  
Vol 108-111 ◽  
pp. 482-487
Author(s):  
Jun Yang ◽  
Wen Pin Luo ◽  
Gui Hua Li
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Descriptor System ◽  
Sampled Data ◽  
Neutral Systems ◽  
Lmi Approach ◽  
Data Control ◽  
System Method ◽  
Sampled Data Control ◽  
Barbalat Lemma

This paper is concerned with the H∞ sampled-data control for a class of fuzzy neutral systems. Employing Lyapunov-Krasovskii functional, the input delay approach, the descriptor system method, Barbalat lemma and the LMI approach, a design method of sampled-data state feedback controller for the fuzzy neutral systems is proposed.

Localization and tracking control for mobile welding robot

2014 ◽  
Vol 41 (3) ◽  
pp. 259-265 ◽  
Author(s):  
Qing Tang
Keyword(s):  
Steel Structure ◽  
Tracking Algorithm ◽  
Laser Sensor ◽  
Localization Algorithm ◽  
Welding Robot ◽  
Content Type ◽  
Mobile Welding Robot ◽  
Barbalat Lemma ◽  
Straight Lines ◽  
Localization And Tracking

Purpose – The purpose of this paper is to design the localization and tracking algorithms for our mobile welding robot to carry out the large steel structure welding operations in industrial environment. Design/methodology/approach – Extended Kalman filter, considering the bicycle-modeled robot, is adopted in the localization algorithm. The position and orientation of our mobile welding robot is estimated using the feedback of the laser sensor and the robot motion commands history. A backstepping variable is involved in the tracking algorithm. By introducing a specifically selected Lyapunov function, we proved the tracking algorithm using Barbalat Lemma, which leads the errors of estimated robot states to converge to zero. Findings – The experiments show that the proposed localization method is fast and accurate and the tracking algorithm is robust to track straight lines, circles and other typical industrial curve shapes. The proposed localization and tracking algorithm could be used, but not limited to the mobile welding. Originality/value – Localization problem which is neglected in previous research is very important in mobile welding. The proposed localization algorithm could estimate the robot states timely and accurately, and no additional sensors are needed. Furthermore, using the estimated robot states, we proposed and proved a tracking algorithm for bicycle-modeled mobile robots which could be used in welding as well as other industrial operation scenarios.

scholarly journals Consensus of Second-Order Multiagent Systems with Directed Signed Networks and Communication Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Huiqin Pei ◽  
Qiang Lai ◽  
Guang Li
Keyword(s):  
Multiagent Systems ◽  
Lyapunov Method ◽  
Second Order ◽  
Consensus Problem ◽  
Communication Delays ◽  
Consensus Control ◽  
Signed Networks ◽  
Signed Digraph ◽  
Strongly Connected ◽  
Barbalat Lemma

This paper is concerned with the consensus problem for second-order multiagent systems (MASs) with directed signed networks and local communication delays. First, under a strongly connected directed graph, some properties for signed digraph and the model of second-order MASs are provided. A distributed nonlinear consensus control protocol is proposed for implementing consensus of second-order MASs with signed digraph and communication delay. Then, for structurally balanced and unbalanced networks, the consensus of second-order MASs with directed signed networks and local delays is proved via the Lyapunov method and Barbalat lemma. Simulation examples are given to demonstrate the effectiveness of our results.

A Developed Adaptive Tracking Control Technique for a Four-Rotor Helicopter with External Disturbance

2013 ◽  
Vol 846-847 ◽  
pp. 18-21
Author(s):  
Fei Fei Lu ◽  
Fu Yang Chen ◽  
Ling Cai
Keyword(s):  
Tracking Control ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Control Technique ◽  
Adaptive Compensation ◽  
Adaptive Tracking Control ◽  
Adaptive Technique ◽  
Adaptive Laws ◽  
Barbalat Lemma ◽  
State Tracking

This paper deals with the tracking control problem of attitude angles for a four-rotor helicopter with external disturbance. A new direct adaptive compensation controller and its parameter adaptive laws are designed based on the Lyapunov stability theory, and the designed contorller can not only compensate the disturbance efficiently, but also can make the attitude angles of the four-rotor helicopter track a given reference output. By using the Barbalat lemma, the systems state tracking performance is proofed. Finally, the proposed adaptive technique is evaluated by a simulation example.

Sign in / Sign up

Export Citation Format

Share Document