Finite-time passive filtering for a class of neutral time-delayed systems

2016 ◽  
Vol 39 (8) ◽  
pp. 1139-1145 ◽  
Author(s):  
Xia Chen ◽  
Shuping He
Keyword(s):  
Finite Time ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Combined System ◽  
Delayed Systems ◽  
Finite Time Stability ◽  
Functional Methods ◽  
Exogenous Disturbances ◽  
Error System ◽  
Filtering Problem

In this paper, the finite-time passive filtering problem of a class of neutral time-delayed systems is considered. The exogenous disturbances are unknown but norm bounded. A sufficient condition for passivity and finite-time stability of the combined system is derived and proved by means of Lyapunov functional methods and linear matrix inequalities (LMIs) techniques. The dynamic of the filtering error system is ensured to be finite-time bounded with a prescribed dissipation performance level [Formula: see text]. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

scholarly journals Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Minsong Zhang
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Time Stability ◽  
Quadratic Systems ◽  
Finite Time Stability ◽  
Jump Time ◽  
Stability And Stabilization ◽  
Finite Time Stabilization

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Robust H∞ deconvolution filter for polytopic uncertain systems with distributed delay

2017 ◽  
Vol 40 (11) ◽  
pp. 3368-3376 ◽  
Author(s):  
Weifeng Xia ◽  
Shengyuan Xu
Keyword(s):  
Uncertain Systems ◽  
Distributed Delay ◽  
Functional Method ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Polytopic Uncertain Systems ◽  
Parameter Dependent ◽  
Filtering Problem

This paper is concerned with the robust H∞ deconvolution filtering problem for polytopic uncertain systems with distributed delay. The objective is to design a full-order deconvolution filter such that the filtering error system is not only asymptotically stable, but also satisfies a prescribed H∞ performance level for all uncertainties. Based on employing the parameter-dependent Lyapunov–Krasovskii functional method, a sufficient condition is proposed for solvability of this problem in terms of linear matrix inequalities. In order to reduce the conservatism, two approaches, namely, the integral partitioning approach, and the homogeneous polynomial parameter-dependent matrix approach, are applied. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed methods in this paper.

scholarly journals STABILITY, FINITE-TIME STABILITY AND PASSIVITY CRITERIA FOR DISCRETE-TIME DELAYED NEURAL NETWORKS

2021 ◽  
Vol 19 (3) ◽  
pp. 199
Author(s):  
Sreten Stojanović ◽  
Miloš Stevanović ◽  
Dragan Antić ◽  
Milan Stojanović
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Finite Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Time Stability ◽  
Finite Time Stability ◽  
Forward Difference

In this paper, we present the problem of stability, finite-time stability and passivity for discrete-time neural networks (DNNs) with variable delays. For the purposes of stability analysis, an 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 non-equidistant subintervals. Then, by using the Wirtinger-based inequality, reciprocally and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of LKF are given. In order to relax the existing results, several zero equalities are introduced and stability criteria are proposed in terms of linear matrix inequalities (LMIs). The main objective for the finite-time stability and passivity analysis is how to effectively evaluate the finite-time passivity conditions for DNNs. To achieve this, some weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of LKF, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology.

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.

scholarly journals Finite-time stability of $ q $-fractional damped difference systems with time delay

2021 ◽  
Vol 6 (11) ◽  
pp. 12011-12027
Author(s):  
Jingfeng Wang ◽  
◽  
Chuanzhi Bai
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Gronwall Inequality ◽  
The Novel ◽  
Delayed Systems ◽  
Finite Time Stability ◽  
Difference Systems ◽  
Grönwall Inequality ◽  
Uniqueness Of The Solution

<abstract><p>In this paper, we investigate and obtain a new discrete $ q $-fractional version of the Gronwall inequality. As applications, we consider the existence and uniqueness of the solution of $ q $-fractional damped difference systems with time delay. Moreover, we formulate the novel sufficient conditions such that the $ q $-fractional damped difference delayed systems is finite time stable. Our result extend the main results of the paper by Abdeljawad et al. [A generalized $ q $-fractional Gronwall inequality and its applications to nonlinear delay $ q $-fractional difference systems, J.Inequal. Appl. 2016,240].</p></abstract>

scholarly journals Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Fucheng Liao ◽  
Yingxue Wu ◽  
Xiao Yu ◽  
Jiamei Deng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Tracking Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Error System ◽  
Finite Time Boundedness ◽  
Boundedness Problem ◽  
Time Systems

A finite-time bounded tracking control problem for a class of linear discrete-time systems subject to disturbances is investigated. Firstly, by applying a difference method to constructing the error system, the problem is transformed into a finite-time boundedness problem of the output vector of the error system. In fact, this is a finite-time boundedness problem with respect to the partial variables. Secondly, based on the partial stability theory and the research methods of finite-time boundedness problem, a state feedback controller formulated in form of linear matrix inequality is proposed. Based on this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is presented to illustrate the effectiveness of the controller.

scholarly journals Non-Fragile Robust H∞ Filtering of Takagi-Sugeno Fuzzy Networked Control Systems with Sensor Failures

Sensors ◽  
2019 ◽  
Vol 20 (1) ◽  
pp. 27 ◽  
Author(s):  
Hao Wang ◽  
Shousheng Xie ◽  
Bin Zhou ◽  
Weixuan Wang
Keyword(s):  
Control Systems ◽  
Networked Control Systems ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Networked Control ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Sensor Failures ◽  
Takagi Sugeno ◽  
Filtering Problem

The fault-tolerant robust non-fragile H∞ filtering problem for networked control systems with sensor failures is studied in this paper. The Takagi-Sugeno fuzzy model which can appropriate any nonlinear systems is employed. Based on the model, a filter which can maintain stability and H∞ performance level under the influence of gain perturbation of the filter and sensor failures is designed. Moreover, the gain matrix of sensor failures is converted into a dynamic interval to expand the range of allowed failures. And the sufficient condition for the existence of the desired filter is derived in terms of linear matrix inequalities (LMIs) solutions. Finally a simulation example is given to illustrate the effectiveness of the proposed method.

Parameter-dependent robust H∞ filtering for uncertain two-dimensional discrete systems in the FM second model

2020 ◽  
Vol 37 (4) ◽  
pp. 1114-1132
Author(s):  
Khalid Badie ◽  
Mohammed Alfidi ◽  
Mohamed Oubaidi ◽  
Zakaria Chalh
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Discrete Systems ◽  
Performance Criterion ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Error System ◽  
Parameter Dependent

Abstract This paper deals with the problem of robust $H_{\infty }$ filtering for uncertain two-dimensional discrete systems in the Fornasini–Marchesini second model with polytopic parameter uncertainties. Firstly, a new $H_{\infty }$ performance criterion is derived by exploiting a new structure of the parameter-dependent Lyapunov function. Secondly, based on the criterion obtained, a new condition for the existence of a robust $H_{\infty }$ filter that ensures asymptotic stability, and a prescribed $H_{\infty }$ performance level of the filtering error system, for all admissible uncertainties is established in terms of linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness and advantage of the proposed method.

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

2020 ◽  
pp. 095965182096689
Author(s):  
Xingyu Zhou ◽  
Haoping Wang ◽  
Yang Tian
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Parabolic Type ◽  
Distributed Parameter Systems ◽  
Temperature Control System ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Stability ◽  
Finite Time Stability ◽  
L2 Norm

In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

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