scholarly journals Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1663
Author(s):  
Yiqing Xue ◽  
Ping Zhao
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
State Feedback ◽  
Sufficient Condition ◽  
Positive Systems ◽  
Numerical Examples ◽  
Lyapunov Function Method ◽  
Stability And Stabilization

This paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using the max-separable ISS Lyapunov function method, a sufficient condition on ISS is given for general NIPS. On that basis, the ISS criteria for linear impulsive positive systems (LIPS) and affine nonlinear impulsive positive systems (ANIPS) are given. Through them, ISS properties can be directly judged from the algebraic and differential characteristics of the systems. Then, utilizing the ISS criteria, state-feedback and impulsive controllers are designed for LIPS and ANIPS, respectively, which make the systems input-to-state stabilizable. Lastly, some numerical examples are given to verify the effectiveness of our results.

scholarly journals Permanence and Periodic Solutions for a Two-Patch Impulsive Migration PeriodicN-Species Lotka-Volterra Competitive System

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Zijian Liu ◽  
Chenxue Yang
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Function Method ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Analysis Method ◽  
Competitive System ◽  
Numerical Examples ◽  
Lyapunov Function Method ◽  
Globally Stable

We study a two-patch impulsive migration periodicN-species Lotka-Volterra competitive system. Based on analysis method, inequality estimation, and Lyapunov function method, sufficient conditions for the permanence and existence of a unique globally stable positive periodic solution of the system are established. Some numerical examples are shown to verify our results and discuss the model further.

scholarly journals Hub-Induced Synchronization in Scale-Free Networks with Cluster Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jianbao Zhang ◽  
Zhongjun Ma ◽  
Jinde Cao
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Cluster Structure ◽  
Sufficient Conditions ◽  
Cluster Synchronization ◽  
Numerical Examples ◽  
Scale Free ◽  
Lyapunov Function Method ◽  
Scale Free Networks ◽  
Theoretical Results

A recent research indicated that the corticocortical connectivity network of the cat possesses cluster structure and that each cluster in the network is scale-free and has a most connected hub. Motivated by that research, we slightly modify the network model and derive sufficient conditions for cluster synchronization of the modified network based on Lyapunov function method. The obtained results indicate that cluster synchronization can be induced by the hubs of the scale-free networks. In our opinion, the concept of hub-induced synchronization provides a better understanding of cluster synchronization in scale-free networks. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

scholarly journals Pinning Synchronization of Switched Complex Dynamical Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Liming Du ◽  
Feng Qiao ◽  
Fengying Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Function Method ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Dynamical Networks ◽  
Switching Law ◽  
Arbitrary Switching ◽  
Lyapunov Function Method ◽  
Networks With Switching Topology

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

scholarly journals Independent of delay stabilization using implicit Lyapunov function method

Automatica ◽  
2019 ◽  
Vol 101 ◽  
pp. 103-110
Author(s):  
Konstantin Zimenko ◽  
Denis Efimov ◽  
Andrey Polyakov ◽  
Artem Kremlev
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Lyapunov Function Method

scholarly journals Unique Existence of Globally Asymptotical Input-to-State Stability of Positive Stationary Solution for Impulsive Gilpin-Ayala Competition Model with Diffusion and Delayed Feedback under Dirichlet Zero Boundary Value

2020 ◽  
Author(s):  
Ruofeng Rao
Keyword(s):  
Fixed Point ◽  
Stationary Solution ◽  
Function Method ◽  
Boundary Value ◽  
Reaction Diffusion ◽  
Delayed Feedback ◽  
Competition Model ◽  
Numerical Examples ◽  
Unique Existence ◽  
Lyapunov Function Method

By partly generalizing the Lipschitz condition of existing results to the generalized Lipschitz one, the author utilizes a fixed point theorem, variational method and Lyapunov function method to derive the unique existence of globally asymptotical input-to-state stability of positive stationary solution for Gilpin-Ayala competition model with diffusion and delayed feedback under Dirichlet zero boundary value. Remarkably, it is the first paper to derive the unique existence of the stationary solution of reaction-diffusion Gilpin-Ayala competition model, which is globally asymptotical input-to-state stability. And numerical examples illuminate the effectiveness and feasibility of the proposed methods.

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