scholarly journals Coefficient Matrix Decomposition Method and BIBO Stabilization of Stochastic Systems with Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xia Zhou ◽  
Shouming Zhong
Keyword(s):  
Control Systems ◽  
Time Delays ◽  
Model Transformation ◽  
Stochastic Systems ◽  
Matrix Decomposition ◽  
Coefficient Matrix ◽  
Linear Matrix ◽  
Mean Square ◽  
The Mean ◽  
Delay Dependent

The mean square BIBO stabilization is investigated for the stochastic control systems with time delays and nonlinear perturbations. A class of suitable Lyapunov functional is constructed, combined with the descriptor model transformation and the decomposition technique of coefficient matrix; thus some novel delay-dependent mean square BIBO stabilization conditions are derived. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Finally, three numerical examples are given to demonstrate that the derived conditions are effective and much less conservative than those given in the literature.

scholarly journals Delay-Dependent RobustH∞Filtering of the Takagi-Sugeno Fuzzy Stochastic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Ze Li ◽  
Xin-Hao Yang
Keyword(s):  
Stochastic Systems ◽  
Design Method ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Mean Square Stability ◽  
Error System ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper is concerned with the problem of the robustH∞filtering for the Takagi-Sugeno (T-S) fuzzy stochastic systems with bounded parameter uncertainties. For a given T-S fuzzy stochastic system, this paper focuses on the stochastically mean-square stability of the filtering error system and theH∞performance level of the output error and the disturbance input. The design method for delay-dependent filter is developed based on linear matrix inequalities. Finally, the effectiveness of the proposed methods is substantiated with an illustrative example.

scholarly journals Delay-Dependent Control for Networked Control Systems with Large Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yilin Wang ◽  
Hamid Reza Karimi ◽  
Zhengrong Xiang
Keyword(s):  
Control Systems ◽  
Time Delays ◽  
Networked Control Systems ◽  
Networked Control ◽  
Linear Matrix ◽  
Practical Case ◽  
Time Model ◽  
Long Time ◽  
Delay Dependent ◽  
And Control

We consider the problems of robust stability and control for a class of networked control systems with long-time delays. Firstly, a nonlinear discrete time model with mode-dependent time delays is proposed by converting the uncertainty of time delay into the uncertainty of parameter matrices. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. For a switched system with a known subsystem occurrence probabilities, we give a stochastic stability criterion in terms of linear matrix inequalities (LMIs). Then, we extend the results to a more practical case where the subsystem occurrence probabilities are uncertain. Finally, a simulation example is presented to show the efficacy of the proposed method.

scholarly journals Delay-Dependent Robust Exponential Stability for Uncertain Neutral Stochastic Systems with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Weihua Mao ◽  
Feiqi Deng ◽  
Anhua Wan
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Robust Exponential Stability ◽  
Interval Time ◽  
Time Varying Delay ◽  
Mean Square Exponential Stability ◽  
Delay Dependent

This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs). By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

ROBUST EXPONENTIAL STABILITY OF STOCHASTIC TIME-DELAY SYSTEMS WITH UNCERTAINTIES AND NONLINEAR PERTURBATIONS

2009 ◽  
Vol 06 (01) ◽  
pp. 61-71 ◽  
Author(s):  
HUAICHENG YAN ◽  
MAX Q.-H. MENG ◽  
XINHAN HUANG ◽  
HAO ZHANG
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Mean Square ◽  
Nonlinear Perturbations ◽  
Robust Exponential Stability ◽  
Mean Square Stability ◽  
Delay Dependent

In this paper, the delay-dependent robust exponential mean-square stability analysis problem is considered for a class of uncertain stochastic systems with time-varying delay and nonlinear perturbations. Some sufficient conditions on delay-dependent robust exponential stability in the mean square are established in terms of linear matrix inequalities (LMIs) by exploiting a novel Lyapunov–Krasovskii functional and by making use of zero equations methods. These developed results indicate less conservatism than the existing ones due to the introduction of some free weighting matrices which can be selected properly. The new delay-dependent stability criteria are expressed as a set of LMIs, which can be readily solved by using standard numerical software. Numerical examples are provided to demonstrate the effectiveness and the applicability of the proposed criteria.

Improved Delay-Dependent Robust Stability Criteria for Discrete-Time Stochastic Uncertain Networks with Time-Varying Delays

2012 ◽  
Vol 430-432 ◽  
pp. 849-852
Author(s):  
Meng Zhuo Luo ◽  
Shou Ming Zhong
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Time Varying ◽  
Mean Square ◽  
Stability Criteria ◽  
The Mean ◽  
Delay Dependent ◽  
Uncertain Networks ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

In this paper, the mean square asymptotical stability is investigated for a class of discrete-time stochastic systems with time-varying delays and norm-bounded uncertainties,a numerical example is presented to show the usefulness of the derived LMI-based stability condition.

scholarly journals Fault Detection for Wireless Networked Control Systems with Stochastic Uncertainties and Multiple Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Lina Rong ◽  
Chengda Yu ◽  
Pengfei Guo ◽  
Hui Gao
Keyword(s):  
Fault Detection ◽  
Control Systems ◽  
Time Delays ◽  
Networked Control Systems ◽  
Networked Control ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
System States ◽  
Stochastic Uncertainties

The fault detection problem for a class of wireless networked control systems is investigated. A Bernoulli distributed parameter is introduced in modeling the system dynamics; moreover, multiple time delays arising in the communication are taken into account. The detection observer for tracking the system states is designed, which generates both the state errors and the output errors. By adopting the linear matrix inequality method, a sufficient condition for the stability of wireless networked control systems with stochastic uncertainties and multiple time delays is proposed, and the gain of the fault detection observer is obtained. Finally, an illustrated example is provided to show that the observer designed in this paper tracks the system states well when there is no fault in the systems; however, when fault happens, the observer residual signal rises rapidly and the fault can be quickly detected, which demonstrate the effectiveness of the theoretical results.

A DELAY-DEPENDENT APPROACH TO ROBUST TAKAGI–SUGENO FUZZY CONTROL OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2011 ◽  
Vol 20 (08) ◽  
pp. 1571-1589 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Fuzzy Control ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper deals with the problem of globally delay-dependent robust stabilization for Takagi–Sugeno (T–S) fuzzy neural network with time delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Based on Lyapunov–Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions are derived for ensuring the exponential stability for the closed-loop fuzzy control system. An important feature of the result is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using the proposed techniques for achieving delay dependence. Another feature of the results lies in that involves fewer matrix variables. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design methods.

Global dissipativity of stochastic Lotka–Volterra system with feedback controls

2017 ◽  
Vol 10 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Qimin Zhang ◽  
Xinjing Zhang ◽  
Hongfu Yang
Keyword(s):  
Linear Matrix Inequalities ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Volterra System ◽  
Feedback Controls ◽  
The Mean

In this paper, a class of stochastic Lotka–Volterra system with feedback controls is considered. The purpose is to establish some criteria to ensure the system is globally dissipative in the mean square. By constructing suitable Lyapunov functions as well as combining with Jensen inequality and It[Formula: see text] formula, the sufficient conditions are established and they are expressed in terms of the feasibility to a couple linear matrix inequalities (LMIs). Finally, the main results are illustrated by examples.

scholarly journals RobustH∞Filtering for Uncertain Neutral Stochastic Systems with Markovian Jumping Parameters and Time Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Yajun Li ◽  
Zhaowen Huang
Keyword(s):  
Time Delay ◽  
Stochastic Systems ◽  
Filter Design ◽  
Linear Matrix ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Stochastically Stable ◽  
Neutral Stochastic Systems ◽  
Error System ◽  
Delay Dependent

This paper deals with the robustH∞filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribedH∞performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.

scholarly journals Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 815 ◽  
Author(s):  
Usa Humphries ◽  
Grienggrai Rajchakit ◽  
Pramet Kaewmesri ◽  
Pharunyou Chanthorn ◽  
Ramalingam Sriraman ◽  
...  
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Time Delays ◽  
System Model ◽  
Mean Square ◽  
New Class ◽  
Quaternion Multiplication ◽  
The Mean ◽  
Theoretical Results

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.

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