Pth moment input-to-state stability of stochastic impulsive switched delayed systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3468-3476
Author(s):  
Lijun Gao ◽  
Shengyan Wang
Keyword(s):  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Delayed Systems ◽  
Stable Function ◽  
Exponentially Stable ◽  
Delayed System ◽  
The Relationship ◽  
Delayed Impulses ◽  
Moment Integral

This paper investigates the pth moment input-to-state stability (ISS) and the pth moment integral input-to-state stability (iISS) of stochastic impulsive switched delayed system with delayed impulses. By employing the method of multiple Lyapunov-Krasovskii functionals and the uniformly exponentially stable function, some relaxed Krasovskii-type sufficient conditions ensuring the pISS/piISS of the addressed systems are developed. These conditions imply the relationship among the impulsive frequency, the time delay existing in impulses, and the coefficients of the estimated upper bound for the derivative of a Lyapunov function. It is shown that if the continuous stochastic delayed dynamics is ISS, and the impulsive effects are destabilizing, then the stochastic impulsive switched delayed system is ISS with respect to the relationship. Compared with the existing results, the conditions obtained results have three relaxations, that is, the derivative of Lyapunov functions of subsystems are allowed to be sign-changing time-varying function rather than a negative definite constant, all subsystems are allowed to be unstable, and the effect of delayed impulses are considered. Finally, an example is provided to illustrate the effectiveness of the results.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

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.

Asymptotic Stabilization of Delayed Systems with Input and Output Saturations

2017 ◽  
Vol 6 (2) ◽  
pp. 63
Author(s):  
Adel Mahjoub ◽  
Nabil Derbel
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Delayed Systems ◽  
Asymptotic Stabilization ◽  
Input And Output ◽  
Delayed System ◽  
The Stability

We consider in this paper the problem of controlling an arbitrary linear delayed system with saturating input and output. We study the stability of such a system in closed-loop with a given saturating regulator. Using inputoutput stability tools, we formulated sufficient conditions ensuring global asymptotic stability.

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.

Asymptotic Stabilization of Delayed Systems with Input and Output Saturations

2017 ◽  
Vol 6 (2) ◽  
pp. 64
Author(s):  
Adel Mahjoub ◽  
Nabil Derbel
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Input Output ◽  
Delayed Systems ◽  
Output Stability ◽  
Input And Output ◽  
Delayed System ◽  
The Stability

We consider in this paper the problem of controlling an arbitrary linear delayed system with saturating input and output. We study the stability of such a system in closed-loop with a given saturating regulator. Using input-output stability tools, we formulated sufficient conditions ensuring global asymptotic stability.

Time-varying H∞ filtering for discrete-time switched systems with admissible edge-dependent average dwell time

2020 ◽  
Vol 42 (14) ◽  
pp. 2719-2732
Author(s):  
Bingxin Xue ◽  
Ruihua Wang ◽  
Shumin Fei
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Switched Systems ◽  
Dwell Time ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Time Varying ◽  
Text Filtering ◽  
Exponentially Stable

This paper addresses the [Formula: see text] filtering problem for a class of discrete-time switched systems by using an admissible edge-dependent average dwell time (AED-ADT) method. By means of a convex combination of positive definite matrices, a novel multiple piecewise convex Lyapunov function (MPCLF) is constructed, which can loosen the restrictions of Lyapunov function at switching points and interval interior points. Based on the MPCLF approach, sufficient conditions are established such that the filtering error system is globally uniformly exponentially stable (GUES) and a prescribed noise attenuation level in an [Formula: see text] sense is achieved. Moreover, the corresponding time-varying [Formula: see text] filters are given as well. Finally, the results of the simulation illustrate the feasibility and effectiveness of the proposed approaches.

scholarly journals Synchronization of Caputo fractional neural networks with bounded time variable delays

2021 ◽  
Vol 19 (1) ◽  
pp. 388-399
Author(s):  
Ricardo Almeida ◽  
Snezhana Hristova ◽  
Stepan Tersian
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Time Variable ◽  
Rate Of Change ◽  
Time Varying ◽  
Time Varying Delay ◽  
Variable Delays ◽  
Varying Delay

Abstract One of the main problems connected with neural networks is synchronization. We examine a model of a neural network with time-varying delay and also the case when the connection weights (the influential strength of the j j th neuron to the i i th neuron) are variable in time and unbounded. The rate of change of the dynamics of all neurons is described by the Caputo fractional derivative. We apply Lyapunov functions and the Razumikhin method to obtain some sufficient conditions to ensure synchronization in the model. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. We illustrate our theory with a particular nonlinear neural network.

Robust Stability of Switched Interconnected Systems With Time-Varying Delays

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Huanbin Xue ◽  
Jiye Zhang ◽  
Hong Wang ◽  
Baoshan Jiang
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Sufficient Conditions ◽  
Interconnected Systems ◽  
Time Varying ◽  
Differential Inequalities ◽  
Interconnected System ◽  
Robust Exponential Stability ◽  
Arbitrary Switching

The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and time-varying delays is investigated. On the assumption that each isolated subsystem of the interconnected system can be exponentially stabilized and the corresponding Lyapunov functions are available, using M-matrix property, the differential inequalities with time-varying delays are constructed. By the stability analysis of the differential inequalities, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems (SIS) under arbitrary switching are obtained. The proposed method, which neither requires the individual subsystems to share a common Lyapunov function (CLF), nor needs to know the values of individual Lyapunov functions at each switching time, would provide a new mentality for studying stability of arbitrary switching. In addition, by resorting to average dwell time approach, conditions for guaranteeing the robust exponential stability of SIS under constrained switching are derived. The proposed criteria are explicit, and they are convenient for practical applications. Finally, two numerical examples are given to illustrate the validity and correctness of the proposed theories.

scholarly journals The Method of Lyapunov Function and Exponential Stability of Impulsive Delay Systems with Delayed Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Pei Cheng ◽  
Feiqi Deng ◽  
Lianglong Wang
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Impulsive Systems ◽  
Lyapunov Function Method ◽  
Impulsive Delay ◽  
Delayed Impulses

This paper investigates the exponential stability of general impulsive delay systems with delayed impulses. By using the Lyapunov function method, some Lyapunov-based sufficient conditions for exponential stability are derived, which are more convenient to be applied than those Razumikhin-type conditions in the literature. Their applications to linear impulsive systems with time-varying delays are also proposed, and a set of sufficient conditions for exponential stability is provided in terms of matrix inequalities. Meanwhile, two examples are discussed to illustrate the effectiveness and advantages of the results obtained.

Dynamical Behaviors of a Large Class of General Delayed Neural Networks

2005 ◽  
Vol 17 (4) ◽  
pp. 949-968 ◽  
Author(s):  
Tianping Chen ◽  
Wenlian Lu ◽  
Guanrong Chen
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Dynamical Systems ◽  
Large Class ◽  
Delayed Systems ◽  
Delayed Neural Networks ◽  
Dynamical Behaviors ◽  
Special Cases ◽  
Exponentially Stable ◽  
Delayed System

Research of delayed neural networks with varying self-inhibitions, interconnection weights, and inputs is an important issue. In the real world, self-inhibitions, interconnection weights, and inputs should vary as time varies. In this letter, we discuss a large class of delayed neural networks with periodic inhibitions, interconnection weights, and inputs. We prove that if the activation functions are of Lipschitz type and some set of inequalities, for example, the set of inequalities 3.1 in theorem 1, is satisfied, the delayed system has a unique periodic solution, and any solution will converge to this periodic solution. We also prove that if either set of inequalities 3.20 in theorem 2 or 3.23 in theorem 3 is satisfied, then the system is exponentially stable globally. This class of delayed dynamical systems provides a general framework for many delayed dynamical systems. As special cases, it includes delayed Hopfield neural networks and cellular neural networks as well as distributed delayed neural networks with periodic self-inhibitions, interconnection weights, and inputs. Moreover, the entire discussion applies to delayed systems with constant self-inhibitions, interconnection weights, and inputs.

Sign in / Sign up

Export Citation Format

Share Document