Observer-Based Stabilization of Linear Discrete Time-Varying Delay Systems

2021 ◽  
Author(s):  
Venkatesh Modala ◽  
Sourav Patra ◽  
Goshaidas Ray
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stabilizing Controller ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Summation Inequality ◽  
Delay Dependent

Abstract This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov-Krasovskii (LK) functional to derive a delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus, ensure global asymptotic stability in presence of any time delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

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 and Stabilization for Singular Time-Delay Systems with Linear Fractional Uncertainties: A Strict LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jinxing Lin ◽  
Lina Rong
Keyword(s):  
Robust Stability ◽  
Singular Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Stabilizing Controller ◽  
Time Varying Delay ◽  
Stability And Stabilization ◽  
Delay Dependent ◽  
Robust Stability And Stabilization

This paper is concerned with the problems of delay-dependent robust stability and stabilization for a class of continuous singular systems with time-varying delay in range and parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. In terms of strict linear matrix inequalities (LMIs), delay-range-dependent robust stability criteria for the unforced system are presented. Moreover, a strict LMI design approach is developed such that, when the LMI is feasible, a desired state feedback stabilizing controller can be constructed, which guarantees that, for all admissible uncertainties, the closed-loop dynamics will be regular, impulse free, and robustly asymptotically stable. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.

scholarly journals Novel Delay-Dependent Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sreten Stojanovic ◽  
Milan Stojanovic ◽  
Milos Stevanovic
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Reciprocally Convex Combination ◽  
Delay Dependent ◽  
Delay Dependent Stability

The delay-dependent stability problem is investigated for discrete-time neural networks with time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two nonequidistant subintervals to derive less conservative stability conditions. Then, by using Wirtinger-based inequality, reciprocally, and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of the LKF are given. Several zero equalities are introduced to further relax the existing results. Less conservative stability criteria are proposed in terms of linear matrix inequalities (LMIs). Finally, numerical examples are proposed to show the effectiveness and less conservativeness of the proposed method.

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.

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 Robust Admissibilization for Discrete-Time Singular Systems with Time-Varying Delay

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Dongdong Wang ◽  
Shengzhi Han ◽  
Jian Chen
Keyword(s):  
Discrete Time ◽  
Singular Systems ◽  
Robust Stabilization ◽  
Feedback Stabilization ◽  
Relaxation Techniques ◽  
Time Varying ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Summation Inequality ◽  
Varying Delay

The problems of the admissibility and state feedback stabilization for discrete-time singular systems with interval time-varying delay and norm-bounded uncertainty are studied. The system is equivalently transformed into a new comparison form by decomposition. By taking advantage of the Seuret summation inequality, the reciprocally convex inequality, and some relaxation techniques, a delay-dependent criterion that ensures the admissibility of the concerned systems is established. The result on robust stabilization is also obtained by fixing some parameters. It should be pointed out that the results are less dependent on the parameters so that some conservatism is reduced. A numerical example is included to illustrate the effectiveness and improvement of the proposed methods.

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.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

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