scholarly journals RobustH∞Filtering for Uncertain Discrete-Time Fuzzy Stochastic Systems with Sensor Nonlinearities and Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Mingang Hua ◽  
Pei Cheng ◽  
Juntao Fei ◽  
Jianyong Zhang ◽  
Junfeng Chen
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Error System ◽  
Varying Delay

The robust filtering problem for a class of uncertain discrete-time fuzzy stochastic systems with sensor nonlinearities and time-varying delay is investigated. The parameter uncertainties are assumed to be time varying norm bounded in both the state and measurement equations. By using the Lyapunov stability theory and some new relaxed techniques, sufficient conditions are proposed to guarantee the robustly stochastic stability with a prescribedH∞performance level of the filtering error system for all admissible uncertainties, sensor nonlinearities, and time-varying delays. These conditions are dependent on the lower and upper bounds of the time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods.

scholarly journals Filtering for Discrete-Time Stochastic Systems with Nonlinear Sensor and Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Mingang Hua ◽  
Pei Cheng ◽  
Juntao Fei ◽  
Jianyong Zhang ◽  
Junfeng Chen
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Time Varying ◽  
Lower And Upper Bounds ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Filtering Problem

The filtering problem for a class of discrete-time stochastic systems with nonlinear sensor and time-varying delay is investigated. By using the Lyapunov stability theory, sufficient conditions are proposed to guarantee the asymptotical stablity with an prescribe performance level of the filtering error systems. These conditions are dependent on the lower and upper bounds of the discrete time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

scholarly journals Nonfragile RobustH∞Filter Design for a Class of Fuzzy Stochastic Systems with Stochastic Input-to-State Stability

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Ze Li ◽  
Feng Gu ◽  
Yuqing He ◽  
Wanjun Hao
Keyword(s):  
Stochastic Systems ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Error System ◽  
Stochastic Input ◽  
Takagi Sugeno ◽  
Varying Delay

The nonfragileH∞filtering problem for a kind of Takagi-Sugeno (T-S) fuzzy stochastic system which has a time-varying delay and parameter uncertainties has been studied in this paper. Sufficient conditions for stochastic input-to-state stability (SISS) of the fuzzy stochastic systems are obtained. Attention is focused on the design of a nonfragileH∞filter such that the filtering error system can tolerate some level of the gain variations in the filter and theH∞performance level also could be satisfied. By using the SISS result, the approach to design the nonfragile filter is proposed in terms of linear matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.

scholarly journals Robust Exponential Stability for LPD Discrete-Time System with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Kanit Mukdasai
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Robust Exponential Stability ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust exponential stability for uncertain linear-parameter dependent (LPD) discrete-time system with delay. The delay is of an interval type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on combination of the linear matrix inequality (LMI) technique and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust exponential stability are obtained in terms of LMI. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

scholarly journals Robust H∞ Observer-Based Control Design for Discrete-Time Nonlinear Systems With Time-Varying Delay

2021 ◽  
Vol 20 ◽  
pp. 88-97
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the problem of robust H∞ observer-based control for a class of discrete-time nonlinear systems with time-varying delays and parameters uncertainties. We propose an observer-based controller. By constructing an appropriate Lyapunov-Krasovskii functional, some sufficient conditions are developed to ensure the closed-loop system is robust asymptotically stable with H∞ performance in terms of the linear matrix inequalities. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

Fuzzy Control of a Class of Discrete-Time Fuzzy Bilinear Systems with Time-Delay

2012 ◽  
Vol 482-484 ◽  
pp. 1881-1885
Author(s):  
Jian Hu Jiang ◽  
Chao Wu ◽  
Yun Wang Ge ◽  
Li Jun Song
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Bilinear System ◽  
Stability Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

The stability control problem is considered for a class of discrete-time T-S fuzzy bilinear system with time-varying delay in both state and input. Based on the parallel distribute compensation (PDC) scheme, some sufficient conditions are derived to guarantee the global asymptotically stability of the overall fuzzy system, which are represented in terms of matrix inequality. The corresponding controller can be obtained by solving a set of linear matrix inequalities. Finally, a simulation example shows that the approach is effective.

scholarly journals Finite-time Stochastic Stability and Stabilization for Uncertain Discrete-time Stochastic Systems with Time-varying Delay

2021 ◽  
Vol 20 ◽  
pp. 244-251
Author(s):  
Xinyue Tang ◽  
Yali Dong ◽  
Meng Liu
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Finite Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Time Varying ◽  
Time Varying Delay ◽  
Stability And Stabilization ◽  
Varying Delay

This paper deals with the problems of finite-time stochastic stability and stabilization for discrete-time stochastic systems with parametric uncertainties and time-varying delay. Using the Lyapunov-Krasovskii functional method, some sufficient conditions of finite-time stochastic stability for a class of discrete-time stochastic uncertain systems are established in term of matrix inequalities. Then, a new criterion is proposed to ensure the closed-loop system is finite-time stochastically stable. The controller gain is designed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.

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 Further Results Concerning Delay-DependentH∞Control for Uncertain Discrete-Time Systems with Time-Varying Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-24 ◽  
Author(s):  
Guangdeng Zong ◽  
Linlin Hou ◽  
Hongyong Yang
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Varying Delay

This paper addresses the problem ofH∞control for uncertain discrete-time systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and controlled output. Attention is focused on the design of a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and reduces the effect of the disturbance input on the controlled output to a prescribed level irrespective of all the admissible uncertainties. By introducing some slack matrix variables, new delay-dependent conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to show the reduced conservatism and lower computational burden than the previous results.

scholarly journals Delay-Range-Dependent Global Robust Passivity Analysis of Discrete-Time Uncertain Recurrent Neural Networks with Interval Time-Varying Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Chien-Yu Lu ◽  
Chin-Wen Liao ◽  
Hsun-Heng Tsai
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Time Varying Delay ◽  
Passivity Analysis ◽  
Varying Delay

This paper examines a passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with norm-bounded time-varying parameter uncertainties and interval time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. Based on an appropriate type of Lyapunov functional, sufficient passivity conditions for the DRNNs are derived in terms of a family of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness and applicability.

scholarly journals RobustH∞Control for a Class of Discrete Time-Delay Stochastic Systems with Randomly Occurring Nonlinearities

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yamin Wang ◽  
Fuad E. Alsaadi ◽  
Stanislao Lauria ◽  
Yurong Liu
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Attenuation Level ◽  
Discrete Time Delay ◽  
And Control

In this paper, we consider the robustH∞control problem for a class of discrete time-delay stochastic systems with randomly occurring nonlinearities. The parameter uncertainties enter all the system matrices; the stochastic disturbances are both state and control dependent, and the randomly occurring nonlinearities obey the sector boundedness conditions. The purpose of the problem addressed is to design a state feedback controller such that, for all admissible uncertainties, nonlinearities, and time delays, the closed-loop system is robustly asymptotically stable in the mean square, and a prescribedH∞disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and stochastic analysis tools, a linear matrix inequality (LMI) approach is developed to derive sufficient conditions ensuring the existence of the desired controllers, where the conditions are dependent on the lower and upper bounds of the time-varying delays. The explicit parameterization of the desired controller gains is also given. Finally, a numerical example is exploited to show the usefulness of the results obtained.

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