The variational Lyapunov function and strict stability theory for differential systems

The aim of this paper is to extend Artstein's theorem on the stabilization of affine in the control nonlinear deterministic systems to nonlinear stochastic differential systems when both the drift and the diffusion terms are affine in the control. We prove that the existence of a smooth control Lyapunov function implies smooth stabilizability.

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Strict Stability Criteria for Impulsive Functional Differential Systems

Journal of Inequalities and Applications ◽

10.1155/2008/243863 ◽

2008 ◽

Vol 2008 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Kaien Liu ◽

Guowei Yang

Keyword(s):

Stability Criteria ◽

Differential Systems ◽

Functional Differential Systems ◽

Strict Stability ◽

Functional Differential

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Analysis of asymptotic equilibrium state of differential systems using Lyapunov function method

2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP) ◽

10.1109/scp.2015.7342054 ◽

2015 ◽

Cited By ~ 2

Author(s):

Alexander V. Ekimov ◽

Michail V. Svirkin

Keyword(s):

Lyapunov Function ◽

Equilibrium State ◽

Function Method ◽

Differential Systems ◽

Lyapunov Function Method ◽

Asymptotic Equilibrium

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Chaos control and anticontrol of a tachometer system by Ge—Yao—Chen partial region stability theory

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes1249 ◽

2008 ◽

Vol 223 (5) ◽

pp. 1069-1082

Author(s):

Z-M Ge ◽

C-Y Chiang

Keyword(s):

Lyapunov Function ◽

Numerical Simulations ◽

Stability Theory ◽

Chaos Control ◽

Homogeneous Function ◽

Lower Degree ◽

Partial Region ◽

Simulation Results

In this paper, chaos control and anticontrol of a tachometer system by Ge—Yao—Chen (GYC) partial region stability are proposed. The Lyapunov function becomes a simple linear homogeneous function and the controllers become simpler by using the GYC partial region stability theory. The simulation results are more precise because the controllers are in lower degree than that of traditional controllers. Finally, chaos control and anticontrol of the tachometer system by GYC partial region stability are obtained and verified by numerical simulations.

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Application of lyapunov function method to the design of variable structure control for a class of measure differential systems with impulsive disturbances *

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)56203-5 ◽

1999 ◽

Vol 32 (2) ◽

pp. 1202-1207

Author(s):

Dong Yue ◽

Shifan Xu

Keyword(s):

Lyapunov Function ◽

Function Method ◽

Variable Structure Control ◽

Variable Structure ◽

Differential Systems ◽

Structure Control ◽

Lyapunov Function Method ◽

Impulsive Disturbances

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The complete synchronization of coupled Morris–Lecar neurons with chemical synapses

International Journal of Modern Physics B ◽

10.1142/s021797921650096x ◽

2016 ◽

Vol 30 (17) ◽

pp. 1650096 ◽

Cited By ~ 3

Author(s):

Guanping Wang ◽

Wuyin Jin ◽

An Wang

Keyword(s):

Lyapunov Function ◽

Stability Theory ◽

Analytical Approach ◽

Model Solution ◽

Sufficient Condition ◽

Neuronal System ◽

Complete Synchronization ◽

Basic Principles ◽

Chemical Synapses

Based on the basic principles of stability theory and Lyapunov function, the condition of complete synchronization in coupled Morris–Lecar (ML) neuronal system with chemical synapses is studied in this work. The boundedness of the model solution is proved by analytical approach, the sufficient condition of the complete synchronization is proposed based on the quadratic of the constructed Lyapunov function and the result is verified by simulations.

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