Robust Exponential Stability of Large-Scale System With Mixed Input Delays and Impulsive Effect

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Huanbin Xue ◽  
Jiye Zhang ◽  
Weifan Zheng ◽  
Wang Hong
Keyword(s):  
Exponential Stability ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Impulsive Effect ◽  
Differential Inequalities ◽  
Robust Exponential Stability ◽  
Large Scale System ◽  
Closed Loop Systems ◽  
The Stability ◽  
Input Delays

In this paper, a class of large-scale systems with impulsive effect, input disturbance, and both variable and unbounded delays were investigated. On the assumption that all subsystems of the large-scale system can be exponentially stabilized, and the stabilizing feedbacks and corresponding Lyapunov functions (LFs) for the closed-loop systems are available, using the idea of vector Lyapunov method and M-matrix property, the intero-differential inequalities with variable and unbounded delays were constructed. By the stability analysis of the intero-differential inequalities, the sufficient conditions to ensure the robust exponential stability of the large-scale system were obtained. Finally, the correctness and validity of the methods was verified by two numerical examples.

scholarly journals Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Huanbin Xue ◽  
Yiqiang Peng ◽  
Quan Xu ◽  
Jibin Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Interval Parameter ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
The Stability ◽  
Complex Valued

In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex number domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example.

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.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

scholarly journals A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with time-varying delays

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
M. Iswarya ◽  
R. Raja ◽  
G. Rajchakit ◽  
J. Cao ◽  
J. Alzabut ◽  
...  
Keyword(s):  
Neural Networks ◽  
Graph Theory ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Lyapunov Functional ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Theoretic Approach ◽  
Discrete Time Delay

AbstractIn this work, the exponential stability problem of impulsive recurrent neural networks is investigated; discrete time delay, continuously distributed delay and stochastic noise are simultaneously taken into consideration. In order to guarantee the exponential stability of our considered recurrent neural networks, two distinct types of sufficient conditions are derived on the basis of the Lyapunov functional and coefficient of our given system and also to construct a Lyapunov function for a large scale system a novel graph-theoretic approach is considered, which is derived by utilizing the Lyapunov functional as well as graph theory. In this approach a global Lyapunov functional is constructed which is more related to the topological structure of the given system. We present a numerical example and simulation figures to show the effectiveness of our proposed work.

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 Exponential Stability and Periodicity of Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guowei Yang ◽  
Yonggui Kao ◽  
Changhong Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Impulsive Effect ◽  
Time Varying ◽  
Delayed Reaction

This paper considers dynamical behaviors of a class of fuzzy impulsive reaction-diffusion delayed cellular neural networks (FIRDDCNNs) with time-varying periodic self-inhibitions, interconnection weights, and inputs. By using delay differential inequality,M-matrix theory, and analytic methods, some new sufficient conditions ensuring global exponential stability of the periodic FIRDDCNN model with Neumann boundary conditions are established, and the exponential convergence rate index is estimated. The differentiability of the time-varying delays is not needed. An example is presented to demonstrate the efficiency and effectiveness of the obtained results.

Large-Scale Uncertain Systems Under Insufficient Decentralized Controllers

1989 ◽  
Vol 111 (3) ◽  
pp. 359-363 ◽  
Author(s):  
Y. H. Chen
Keyword(s):  
Dynamical Systems ◽  
Uncertain Systems ◽  
Large Scale ◽  
Large Scale System ◽  
Uncertain Dynamical Systems ◽  
Partial Stability ◽  
Decentralized Controllers ◽  
Total Stability ◽  
The Stability

We consider a class of large-scale uncertain dynamical systems under decentralized controllers. The system is composed of N interconnected subsystems which possess uncertainty. Moreover, there are uncertainties in the interconnections. If the subsystems are under sufficient decentralized controllers, the large-scale system is practically stable. As certain controllers fail, study on the conditions for total stability of partial stability to be preserved is made. It can be shown that the stability is only related to bound of uncertainty and the structure of the large-scale system. Moreover, the conditions can be utilized to determine the importance of some controllers for stability.

Intelligent fuzzy algorithm for nonlinear discrete-time systems

2019 ◽  
Vol 42 (7) ◽  
pp. 1358-1374
Author(s):  
Tim Chen ◽  
CYJ Chen
Keyword(s):  
Large Scale ◽  
Optimal Solution ◽  
Bat Algorithm ◽  
Linear Matrix ◽  
Neural Network Modeling ◽  
Rule Base ◽  
Large Scale System ◽  
Model Based ◽  
Linear Differential ◽  
The Stability

This paper is concerned with the stability analysis and the synthesis of model-based fuzzy controllers for a nonlinear large-scale system. In evolved fuzzy NN (neural network) modeling, the NN model and LDI (linear differential inclusion) representation are established for the arbitrary nonlinear dynamics. The evolved bat algorithm (EBA) is first incorporated in the controlled algorithm of stability conditions, which could rapidly find the optimal solution and raise the control performance. This representation is constructed by taking advantage of sector nonlinearity that converts the nonlinear model to a multiple rule base linear model. A new sufficient condition guaranteeing asymptotic stability is implemented via the Lyapunov function in terms of linear matrix inequalities. Subsequently, based on this criterion and the decentralized control scheme, an evolved model-based fuzzy H infinity set is synthesized to stabilize the nonlinear large-scale system. Finally, a numerical example and simulation is given to illustrate the results.

scholarly journals LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinearp-Laplace Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Ruofeng Rao ◽  
Xiongrui Wang ◽  
Shouming Zhong ◽  
Zhilin Pu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Schur Complement ◽  
Great Difficulty ◽  
Markovian Jumping ◽  
Robust Exponential Stability ◽  
Almost Sure Exponential Stability ◽  
The Stability ◽  
Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinearp-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods inW1,p(Ω),Itôformula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.

Exponential Stability of Stochastic Age-Dependent Population with Diffusion

2011 ◽  
Vol 282-283 ◽  
pp. 231-235
Author(s):  
Hui Li Han ◽  
Qi Min Zhang
Keyword(s):  
Hilbert Space ◽  
Exponential Stability ◽  
Dynamic System ◽  
Population Dynamic ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Exponential Martingale ◽  
Age Dependent ◽  
The Stability

In this paper, a class of stochastic age-dependent population dynamic system with diffusion is introduced. Exponential stability of paths of a strong solution for stochastic age-dependent population dynamic system in Hilbert space is established. The analyses use exponential martingale formula, Lyapunov functional and some special inequalities for our stability purposes. Various sufficient conditions are obtained to ensure the stability of the strong solutions. In particular, by means of our results we loosen the condition of stability.

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