scholarly journals Global exponential stabilization of nonlinear systems via width time-dependent periodically intermittent smooth control

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jitai Liang ◽  
Wanjun Xia
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Time Dependent ◽  
Smooth Control ◽  
Index Function ◽  
Stability And Stabilization ◽  
In Virtue Of ◽  
Theoretical Results

Abstract In this paper, the global exponential stability and stabilization problems for a class of nonlinear systems are investigated. Some sufficient conditions to guarantee global exponential stable and estimate the minimum admissible value of the control width are presented in virtue of time-dependent width Lyapunov functions. Furthermore, a periodically intermittent smooth controller with variant control width is introduced and theoretical analysis is provided. The smooth index function of periodically intermittent smooth control inputs is defined and the supremum (or least upper bound) of smooth index function set can be solved. On the basis of the analysis, the designed periodically intermittent smooth controller not only can globally exponentially stabilize the nonlinear systems, but also can control the exponential convergence rate of the nonlinear systems. Finally, numerical simulations are given to verify the obtained theoretical results.

scholarly journals Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations

2015 ◽  
Vol 25 (4) ◽  
pp. 815-826 ◽  
Author(s):  
Máximo Ramírez ◽  
Raúl Villafuerte ◽  
Temoatzin González ◽  
Miguel Bernal
Keyword(s):  
Nonlinear Systems ◽  
Mimo System ◽  
Sufficient Conditions ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Exponential Estimates ◽  
Novel Approach ◽  
Guaranteed Cost ◽  
Stability And Stabilization ◽  
Twin Rotor Mimo System

Abstract This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov–Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.

scholarly journals An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Kanit Mukdasai ◽  
Piyapong Niamsup
Keyword(s):  
Time Scales ◽  
Lyapunov Functions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Nonlinear Perturbation ◽  
Uniform Stability ◽  
Time Varying ◽  
Lmi Approach ◽  
Theoretical Results

We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, -uniform stability, andh-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results.

scholarly journals Dynamics of a stochastic HIV/AIDS model with treatment under regime switching

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Miaomiao Gao ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Stationary Distribution ◽  
Regime Switching ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Aids Model ◽  
Telegraph Noise ◽  
Spread Dynamics ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Hiv Aids

<p style='text-indent:20px;'>This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.</p>

scholarly journals Interval criterion for stability analysis of discrete-time nonlinear systems with partial state saturation nonlinearities

2006 ◽  
Vol 19 (2) ◽  
pp. 271-286
Author(s):  
Lubomir Kolev ◽  
Simona Filipova-Petrakieva ◽  
Valeri Mladenov
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Positive Definite ◽  
Interval Uncertainties ◽  
Partial State ◽  
Definite Interval ◽  
Outer Bounds ◽  
State Saturation

A generalization of sufficient conditions for global asymptotic stability of the equilibrium of discrete-time nonlinear systems with saturation non linearity's on part of the states in the case of interval uncertainties is considered. When using quadratic form Lyapunov functions, sufficient conditions based on the positive definite interval matrices are presented. In order to check this, a recently proposed method for determining the outer bounds of eigenvalues ranges is used. A numerical example illustrating the applicability of the method suggested is solved in the end of the paper.

Stationary distribution and extinction for a stochastic two-compartment model of B-cell chronic lymphocytic leukemia

2021 ◽  
pp. 2150065
Author(s):  
Miaomiao Gao ◽  
Daqing Jiang ◽  
Xiangdan Wen
Keyword(s):  
Chronic Lymphocytic Leukemia ◽  
Stationary Distribution ◽  
Lyapunov Functions ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Compartment Model ◽  
Lymphocytic Leukemia ◽  
Two Compartment Model ◽  
Theoretical Results ◽  
Cell Chronic Lymphocytic Leukemia

In this paper, we study the dynamical behavior of a stochastic two-compartment model of [Formula: see text]-cell chronic lymphocytic leukemia, which is perturbed by white noise. Firstly, by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Then, conditions for extinction of the disease are derived. Furthermore, numerical simulations are presented for supporting the theoretical results. Our results show that large noise intensity may contribute to extinction of the disease.

scholarly journals Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Cuimei Jiang ◽  
Akbar Zada ◽  
M. Tamer Şenel ◽  
Tongxing Li
Keyword(s):  
Fractional Order ◽  
Lyapunov Functions ◽  
Chaotic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Order Error ◽  
Synchronization Problem ◽  
Direct Design ◽  
Error System ◽  
Theoretical Results

Abstract This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results.

scholarly journals Quadratic Lyapunov Functions for Stability of the Generalized Proportional Fractional Differential Equations with Applications to Neural Networks

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 322
Author(s):  
Ricardo Almeida ◽  
Ravi P. Agarwal ◽  
Snezhana Hristova ◽  
Donal O’Regan
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Lyapunov Functions ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Hopfield Neural Network ◽  
Quadratic Lyapunov Functions ◽  
Fractional Differential ◽  
The Stability ◽  
Theoretical Results

A fractional model of the Hopfield neural network is considered in the case of the application of the generalized proportional Caputo fractional derivative. The stability analysis of this model is used to show the reliability of the processed information. An equilibrium is defined, which is generally not a constant (different than the case of ordinary derivatives and Caputo-type fractional derivatives). We define the exponential stability and the Mittag–Leffler stability of the equilibrium. For this, we extend the second method of Lyapunov in the fractional-order case and establish a useful inequality for the generalized proportional Caputo fractional derivative of the quadratic Lyapunov function. Several sufficient conditions are presented to guarantee these types of stability. Finally, two numerical examples are presented to illustrate the effectiveness of our theoretical results.

scholarly journals Stability for a Class of State Constrained Impulsive Nonlinear Systems: Barrier Lyapunov Functions Method

2021 ◽  
Author(s):  
Liangliang Li ◽  
Zhengwen Tu ◽  
Guanghui Zhou
Keyword(s):  
Nonlinear Systems ◽  
Hybrid Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Invariant Sets ◽  
Inductive Method ◽  
Linear Matrix ◽  
Ellipsoid Method ◽  
Lyapunov Functions Method ◽  
Barrier Lyapunov Functions

Abstract This paper studies the problem for a class of state constrained impulsive nonlinear systems. Firstly, we establish two sufficient conditions for the stability of invariant sets of state constrained hybrid systems. Secondly, we construct the symmetric and asymmetric barrier Lyapunov functions, respectively. A feedback method is presented to solve the stabilization problem of constrained hybrid systems. Introduce the auxiliary matrix, combining with inductive method and linear matrix inequality theory, some sufficient conditions are obtained to ensure stability for state constrained hybrid dynamical networks by the attractive ellipsoid method approach. Finally, one example with simulations is given to validate the effectiveness of the proposed criteria.

scholarly journals Generalized Mutual Synchronization between Two Controlled Interdependent Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Quan Xu ◽  
Shengxian Zhuang ◽  
Dan Hu ◽  
Yingfeng Zeng ◽  
Jian Xiao
Keyword(s):  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Time Varying ◽  
State Variables ◽  
Mutual Synchronization ◽  
Interdependent Networks ◽  
Synchronization Errors ◽  
Simulation Results ◽  
Theoretical Results

This paper mainly focuses on the generalized mutual synchronization between two controlled interdependent networks. First, we propose the general model of controlled interdependent networksAandBwith time-varying internetwork delays coupling. Then, by constructing Lyapunov functions and utilizing adaptive control technique, some sufficient conditions are established to ensure that the mutual synchronization errors between the state variables of networksAandBcan asymptotically converge to zero. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results and to explore potential application in future smart grid. The simulation results also show how interdependent topologies and internetwork coupling delays influence the mutual synchronizability, which help to design interdependent networks with optimal mutual synchronizability.

Stability and Stabilization of a Class of Fractional-Order Nonlinear Systems for 1 < α < 2

2018 ◽  
Vol 13 (3) ◽  
Author(s):  
Sunhua Huang ◽  
Bin Wang
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Jordan Decomposition ◽  
Gronwall’S Inequality ◽  
The Laplace Transform ◽  
Stability And Stabilization ◽  
The Stability ◽  
Order Four

This study is interested in the stability and stabilization of a class of fractional-order nonlinear systems with Caputo derivatives. Based on the properties of the Laplace transform, Mittag-Leffler function, Jordan decomposition, and Grönwall's inequality, some sufficient conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with 1<α<2 are presented. Finally, typical instances, including the fractional-order three-dimensional (3D) nonlinear system and the fractional-order four-dimensional (4D) nonlinear hyperchaos, are implemented to demonstrate the feasibility and validity of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document