scholarly journals Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Fei Chen ◽  
Fei Liu ◽  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Space Representation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Finite Time Stabilization

This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

scholarly journals Finite-Time Stabilization for Stochastic Inertial Neural Networks with Time-Delay via Nonlinear Delay Controller

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Deyi Li ◽  
Yuanyuan Wang ◽  
Guici Chen ◽  
Shasha Zhu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Finite Time ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Feedback ◽  
Inertial Neural Networks ◽  
Finite Time Stabilization

This paper pays close attention to the problem of finite-time stabilization related to stochastic inertial neural networks with or without time-delay. By establishing proper Lyapunov-Krasovskii functional and making use of matrix inequalities, some sufficient conditions on finite-time stabilization are obtained and the stochastic settling-time function is also estimated. Furthermore, in order to achieve the finite-time stabilization, both delayed and nondelayed nonlinear feedback controllers are designed, respectively, in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the correction of the theoretical results and the effectiveness of the proposed control design method.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

scholarly journals Finite-Time Robust Stabilization for Stochastic Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Weixiong Jin ◽  
Xiaoyang Liu ◽  
Xiangjun Zhao ◽  
Nan Jiang ◽  
Zhengxin Wang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stochastic Nonlinear Systems ◽  
Stochastic Neural Networks ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Stabilization

This paper is concerned with the finite-time stabilization for a class of stochastic neural networks (SNNs) with noise perturbations. The purpose of the addressed problem is to design a nonlinear stabilizator which can stabilize the states of neural networks in finite time. Compared with the previous references, a continuous stabilizator is designed to realize such stabilization objective. Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are established for ensuring the finite-time stability of the dynamics of SNNs in probability. Then, the gain parameters of the finite-time controller could be obtained by solving a linear matrix inequality and the robust finite-time stabilization could also be guaranteed for SNNs with uncertain parameters. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.

scholarly journals Finite-Time Nonfragile Dissipative Control for Discrete-Time Neural Networks with Markovian Jumps and Mixed Time-Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Ling Hou ◽  
Dongyan Chen ◽  
Chan He
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Existence Condition ◽  
Mode Switching ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Time Varying Delay ◽  
Mixed Time Delays

This paper considers the stochastic finite-time dissipative (SFTD) control problem based on nonfragile controller for discrete-time neural networks (NNS) with Markovian jumps and mixed delays, in which the mode switching phenomenon, is described as Markov chain, and the mixed delays are composed of discrete time-varying delay and distributed delays. First, by selecting an appropriate Lyapunov-Krasovskii functional and applying stochastic analysis methods, some parameters-dependent sufficient conditions for solvability of stochastic finite-time boundedness are derived. Then, the main results are extended to SFTD control. Furthermore, existence condition of nonfragile controller is derived based on solution of linear matrix inequalities (LMIs). Finally, two numerical examples are employed to show the effectiveness of the obtained methods.

Stochastic Finite-Time Stabilization for Uncertain Jump Systems via State Feedback

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
External Disturbances ◽  
Markov Jump Systems ◽  
Finite State ◽  
Finite Time Stabilization ◽  
Jump Systems

The stochastic finite-time stabilization problem is considered for a class of linear uncertain Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. By using the appropriate stochastic Lyapunov–Krasovskii functional approach, sufficient conditions are proposed for the design of stochastic finite-time stabilization controller. The stabilization criteria are formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The designed finite-time stabilized controller makes the stochastic MJSs stochastic finite-time bounded and stochastic finite-time stabilizable for all admissible unknown external disturbances and uncertain parameters. Simulation results illustrate the effectiveness of the developed approaches.

scholarly journals Robust Finite-time Boundedness of Discrete-time Neural Networks with Time-varying Delays

2021 ◽  
Vol 17 ◽  
pp. 146-155
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

This paper is concerned with the problem of robust finite-time boundedness for the discrete-time neural networks with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii functional, we propose the sufficient conditions which ensure the robust finite-time boundedness of the discrete-time neural networks with time-varying delay in terms of linear matrix inequalities. Then the sufficient conditions of robust finite-time stability for the discrete-time neural networks with time-varying delays are given. Finally, a numerical example is presented to illustrate the efficiency of proposed methods.

scholarly journals Finite-TimeH∞Control for Discrete-Time Markov Jump Systems with Actuator Saturation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Bo Li ◽  
Junjie Zhao
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Finite Time Stability ◽  
Time Control ◽  
Jump Systems

This paper investigates the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. The finite-timeH∞controller via state feedback is designed to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic control performance of discrete-time Markov jump systems are derived in the form of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

scholarly journals State Estimation for Discrete-Time Fuzzy Cellular Neural Networks with Mixed Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Lijie Geng ◽  
Haiying Li ◽  
Bingchen Zhao ◽  
Guang Su
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Discrete Time ◽  
Time Delays ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Fuzzy Cellular Neural Networks ◽  
Mixed Time Delays

This paper is concerned with the exponential state estimation problem for a class of discrete-time fuzzy cellular neural networks with mixed time delays. The main purpose is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. By constructing a novel Lyapunov-Krasovskii functional which contains a triple summation term, some sufficient conditions are derived to guarantee the existence of the state estimator. The linear matrix inequality approach is employed for the first time to deal with the fuzzy cellular neural networks in the discrete-time case. Compared with the present conditions in the form ofM-matrix, the results obtained in this paper are less conservative and can be checked readily by the MATLAB toolbox. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed results.

Finite-Time Stabilization of Stochastic Systems With Partially Known Transition Probabilities

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Xiao-li Luan ◽  
Fei Liu ◽  
Peng Shi
Keyword(s):  
Finite Time ◽  
Stochastic Systems ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Fixed Time ◽  
Linear Matrix ◽  
Time Interval ◽  
Markov Jump ◽  
Stabilizing Controller ◽  
Finite Time Stabilization

In this paper, the problem of finite-time stabilization for a class of uncertain Markov jump systems with partially known transition probabilities is investigated. The main aim of this paper is to derive the finite-time stabilization criteria for the underlying systems when the transition probabilities are partially known and to design a state feedback stabilizing controller such that the trajectories of the system stay within a given bound in a fixed time interval. Sufficient conditions for the existence of the desired controller are established with the linear matrix inequalities framework. A numerical example is used to illustrate the effectiveness of the developed theoretic results.

On robust controllability of uncertain non-linear jump systems with respect to the finite-time interval

2011 ◽  
Vol 34 (7) ◽  
pp. 841-849 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markov Jump ◽  
Non Linear ◽  
Robust Controllability ◽  
Jump Systems ◽  
Takagi Sugeno

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches.

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