scholarly journals A Novel Approach toH∞Control Design for Linear Neutral Time-Delay Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hongwei Xia ◽  
Pingping Zhao ◽  
Li Li ◽  
Aiguo Wu ◽  
Guangcheng Ma
Keyword(s):  
Design Method ◽  
Delay Systems ◽  
Linear Matrix ◽  
Neutral Systems ◽  
Time Varying Delay ◽  
Bounded Real Lemma ◽  
Novel Approach ◽  
Delay Dependent ◽  
Delay Partitioning ◽  
Varying Delay

This paper is concerned with the problem ofH∞control of linear neutral systems with time-varying delay. Firstly, by applying a novel Lyapunov-Krasovskii functional which is constructed with the idea of delay partitioning approach, appropriate free-weighting matrices, an improved delay-dependent bounded real lemma (BRL) for neutral systems is established. By using the obtained BRL, a delay-dependent sufficient condition for the existence of a state-feedback controller, which ensures asymptotic stability and a prescribedH∞performance level of the corresponding closed-loop system, is formulated in terms of linear matrix inequalities. Some numerical examples are given to illustrate the effectiveness of the proposed design method.

Exponential Delay Dependent Stabilization for Time-Varying Delay Systems With Saturating Actuator

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Time Delay ◽  
Design Method ◽  
Delay System ◽  
Rate Of Change ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

This paper deals with the stabilization criteria for a class of time-varying delay systems with saturating actuator. Based on the Lyapunov–Krasovskii functional combining with linear matrix inequality techniques and Leibniz–Newton formula, delay-dependent stabilization criteria are derived using a state feedback controller. We also consider efficient convex optimization algorithms to the time-varying delay system with saturating actuator case: the maximal bound on the time delay such that the prescribed level of operation range and imposed exponential stability requirements are still preserved. The value of the time-delay as well as its rate of change are taken into account in the design method presented and further permit us to reduce the conservativeness of the approach. The results have been illustrated by given numerical examples. These results are shown to be less conservative than those reported in the literature.

scholarly journals Robust Stability Criteria for Uncertain Neutral Systems with Interval Nondifferentiable Time-Varying Delay and Nonlinear Perturbations

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
W. Weera ◽  
P. Niamsup
Keyword(s):  
Robust Stability ◽  
Linear Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

We study the robust stability criteria for uncertain neutral systems with interval time-varying delays and time-varying nonlinear perturbations simultaneously. The constraint on the derivative of the time-varying delay is not required, which allows the time-delay to be a fast time-varying function. Based on the Lyapunov-Krasovskii theory, we derive new delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.

On Stability of Neutral Systems with Time-Varying Delay

2011 ◽  
Vol 50-51 ◽  
pp. 22-26
Author(s):  
Mei Lan Tang ◽  
Xin Ge Liu
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Discrete Delay ◽  
Neutral Systems ◽  
Neutral Delay ◽  
Time Varying Delay ◽  
Discrete Delays ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the delay-dependent robust stability of neutral systems with time-varying discrete delays and time-varying structured uncertainties. New delay-dependent stability criteria are obtained and formulated in the form of a linear matrix inequality. Since the criteria take the sizes of the neutral delay, discrete delay and derivative of discrete delay into account, they are less conservative than previous methods. Numerical example is given to indicate significant improvements over some existing results.

scholarly journals Delay-DependentH∞Control for Descriptor Markovian Jump Systems with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
Jinghao Li ◽  
Qingling Zhang ◽  
Ding Zhai ◽  
Yi Zhang
Keyword(s):  
Convex Combination ◽  
Markovian Jump Systems ◽  
Delay Systems ◽  
Time Varying ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
Bounded Real Lemma ◽  
Delay Dependent ◽  
Jump Systems ◽  
Varying Delay

This paper is concerned with the delay-dependentH∞control problem for continuous-time descriptor Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii functionals for different subsystems, together with delay decomposition method, a new delay-dependent bounded real lemma (BRL) is derived, under which descriptor Markovian jump time-delay systems are regular, impulse-free, and stochastically stable and satisfy a prescribedH∞performance level. Since the reciprocally convex combination approach is adopted to estimate the upper bound of the integral terms, the BRL obtained in this paper is less conservative than some existing ones. Based on the proposed BRL, a sufficient condition for the existence of state feedback controller is provided. Finally, three numerical examples are provided to demonstrate the validity of the proposed methods.

Hysteresis Switching Design for Stabilization of Switched Neutral Systems Using Multiple Lyapunov Functionals

2012 ◽  
Author(s):  
Tai-Fang Li ◽  
Georgi M. Dimirovski ◽  
Jun Zhao
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Neutral Systems ◽  
Switching Law ◽  
Time Varying Delay ◽  
Switched Neutral Systems ◽  
Delay Dependent ◽  
Varying Delay

The stabilization problem for a class of switched neutral systems with a discrete time-varying delay is studied in this paper. The upper bound of derivative of the discrete time-varying delay can be an arbitrary given constant which is not necessary to be less than one. Each subsystem is not assumed to be stable. A hysteresis switching law is designed based on multiple Lyapunov functionals to avoid sliding modes and chattering phenomena. The obtained delay-dependent stabilization criterion is given in terms of linear matrix inequalities (LMIs). The result is illustrated by an example.

Stability Analysis for Linear Systems with Time-Varying Delay

2012 ◽  
Vol 546-547 ◽  
pp. 886-891
Author(s):  
Li Hui Cheng ◽  
Zhan Lei Shang
Keyword(s):  
Stability Analysis ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
System Method ◽  
Sufficient Stability Condition ◽  
Continuous Time Delay ◽  
Delay Dependent ◽  
New Criterion ◽  
Varying Delay

This paper studies the problem of stability analysis for continuous-time delay systems. By introducing a free weighting parameter, combining a novel Lyapunov functional with the switching system method, a new delay-dependent sufficient stability condition is obtained in terms of a linear matrix inequality (LMI). It is shown that this new criterion can provide less conservative results than all existing ones. Numerical examples are given to illustrate the effectiveness and advantages of the proposed method.

scholarly journals A Novel Wirtinger-Based Inequality to H∞ Filtering for Discrete-Time Systems with Time-Varying Delay

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Kaifan Ma ◽  
Zhangang Wang ◽  
Fengdong Shi ◽  
Liankun Sun
Keyword(s):  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Delay Partitioning ◽  
Varying Delay

This article is committed to H∞ filtering for linear discrete-time systems with time-varying delay. The novelty of the paper comes from the consideration of the new Wirtinger-based inequality with double accumulation terms and the idea of delay-partitioning, which guarantees a better asymptotic stability and is less conservative than the celebrated free-weighting matrix or Jensen’s inequality methods. In combination with the improved Wirtinger-based inequality to handle the modified Lyapunov-Krasovskii (L-K) functionals, a new delay-dependent bound real lemma (BRL) is gained. In the light of the derived H∞ performance analysis results, the H∞ filter will be designed in response to linear matrix inequality (LMI). The validness of the proposed methods will be expressed via some numerical examples by the comparison of existing results.

Conservativeness Judgement of Controller for Systems with Time-Varying Delay

2012 ◽  
Vol 249-250 ◽  
pp. 1173-1179
Author(s):  
Jiu Ying Deng ◽  
Hui Fei Deng ◽  
Jian Bin Xiong ◽  
Qin Ruo Wang
Keyword(s):  
Delay System ◽  
Delay Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Optimization Approach ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

The conservatism of asymptotic stability conditions is considered in terms of linear matrix inequalities for time-varying delay systems. The conservative index is defined to evaluate the conservativeness for both delay-dependent and delay-independent stability conditions. The general results on performance analysis are presented based on descriptor system approach. The conservativeness index is defined for time-varying delay system. The optimization approach is given to obtain the upper delay and rational performances for the state-feedback controller of time-delay systems. Experimental results verify the effectiveness of the new method.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

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