scholarly journals Delay-DependentH∞Filtering for Singular Time-Delay Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Zhenbo Li ◽  
Shuqian Zhu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Error System ◽  
Cone Complementarity Linearization ◽  
Delay Dependent ◽  
Singular Time

This paper deals with the problem of delay-dependentH∞filtering for singular time-delay systems. First, a new delay-dependent condition which guarantees that the filter error system has a prescribedH∞performanceγis given in terms of linear matrix inequalities (LMIs). Then, the sufficient condition is obtained for the existence of theH∞filter, and the explicit expression for the desiredH∞filter is presented by using LMIs and the cone complementarity linearization iterative algorithm. A numerical example is provided to illustrate the effectiveness of the proposed method.

Stability of nonlinear time-delay systems satisfying a quadratic constraint

2016 ◽  
Vol 40 (3) ◽  
pp. 712-718 ◽  
Author(s):  
Mohsen Ekramian ◽  
Mohammad Ataei ◽  
Soroush Talebi
Keyword(s):  
Time Delay ◽  
Uncertain Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Quadratic Constraint ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities.

Delay-dependent robust H∞ control for neutral time-delay systems

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
MAN SUN ◽  
AIMIN YANG
Keyword(s):  
Time Delay ◽  
Performance Criterion ◽  
Controller Synthesis ◽  
Delay Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Delay Dependent ◽  
Decoupled Structure

We derive a delay-dependent H∞ performance criterion with a decoupled structure for systems with neutral time delay. We then extend it to an H∞ controller synthesis for systems with polytopic uncertainty. All conditions are given in terms of linear matrix inequalities (LMIs). In some previous descriptor system methods, the products of the controller and Lyapunov matrices are completely separated for the performance analysis, but not for controller synthesis - the method developed in the current paper eliminates this weakness. We present a numerical example to illustrate the effectiveness of the solution.

scholarly journals Robust and NonfragileH∞Kalman-Type Filter Design for Parameter-Uncertain Time-Delay Systems: PLMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Seung Hyeop Yang ◽  
Hong Bae Park
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Parameter Uncertainties

This paper describes the synthesis of a robust and nonfragileH∞Kalman-type filter design for a class of time-delay systems with polytopic uncertainties, filter-gain variations, and disturbances. We present the sufficient condition for filter existence and the method for designing a robust nonfragileH∞filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use a relaxation technique to find finite solutions for a robust nonfragileH∞filter. We show that the proposed filter can minimize estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

scholarly journals Delay-Dependent Stability of Uncertain Distributed Time-Delay Systems

2012 ◽  
Vol 6-7 ◽  
pp. 45-48
Author(s):  
Cheng Wang ◽  
Qing Zhang ◽  
Jian Ping Gan
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Distributed Time Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the problem of stability analysis of uncertain distributed time-delay systems is investigated. Systems with norm-bounded parameter uncertainties are considered. By taking suitable Lyapunov-Krasovskii functional and free weighting matrices, a delay-dependent sufficient condition is derived in terms of linear matrix inequality (LMI). The condition obtained in this paper can be tested numerically very efficiently using interior point algorithms.

Robust H∞ Control of Time-Delay Systems

2013 ◽  
Vol 634-638 ◽  
pp. 3849-3852
Author(s):  
Man Sun
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Performance Criterion ◽  
Delay Systems ◽  
Linear Matrix ◽  
Polytopic Uncertainty ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Feedback Synthesis ◽  
Delay Dependent

In this paper, a delay-dependent H_infinity performance criterion which possess decoupling structure is derived for a class of time-delay systems. It is then extended to H_infinity state-feedback synthesis for time-delay systems with polytopic uncertainty. All the conditions are given in terms of the linear matrix inequalities (LMIs). Numerical examples illustrate the effectiveness of our methods.

scholarly journals Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2441
Author(s):  
Chun-Tang Chao ◽  
Ding-Horng Chen ◽  
Juing-Shian Chiou
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Delay Dependent ◽  
Takagi Sugeno

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

H∞ filter design for singular time-delay systems

2009 ◽  
Vol 223 (7) ◽  
pp. 1001-1015 ◽  
Author(s):  
Z Wu ◽  
H Su ◽  
J Chu
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Delay Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Lmi Approach ◽  
Delay Dependent ◽  
Filtering Problem ◽  
Singular Time

This paper aims to solve the H∞ filtering problem for singular time-delay systems. Two new and improved delay-dependent bounded real lemmas (BRLs), which are equivalent to each other, are proposed. Based on one of them, an H∞ filter is designed via a linear matrix inequality (LMI) approach. Numerical examples are given to illustrate that the newly proposed methods introduce less conservatism than the existing ones.

Linear Quadratic Nash Game of Stochastic Singular Time-Delay Systems with Multiple Decision Makers

2015 ◽  
Vol 3 (5) ◽  
pp. 472-480
Author(s):  
Huainian Zhu ◽  
Guangyu Zhang ◽  
Chengke Zhang ◽  
Ying Zhu ◽  
Haiying Zhou
Keyword(s):  
Time Delay ◽  
Decision Makers ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Linear Quadratic ◽  
Nash Game ◽  
Multiple Decision Makers ◽  
Nash Strategies ◽  
Singular Time

AbstractThis paper discusses linear quadratic Nash game of stochastic singular time-delay systems governed by Itô’s differential equation. Sufficient condition for the existence of Nash strategies is given by means of linear matrix inequality for the first time. Moreover, in order to demonstrate the usefulness of the proposed theory, stochastic H2∕H∞control with multiple decision makers is discussed as an immediate application.

scholarly journals New delay-dependent observer-based control for uncertain stochastic time-delay systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiu-feng Miao ◽  
Long-suo Li
Keyword(s):  
Time Delay ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Noise Disturbances ◽  
System States ◽  
Delay Dependent ◽  
Stochastic Time

AbstractThis paper considers the problem of estimating the state vector of uncertain stochastic time-delay systems, while the system states are unmeasured. The system under study involves parameter uncertainties, noise disturbances and time delay, and they are dependent on the state. Based on the Lyapunov–Krasovskii functional approach, we present a delay-dependent condition for the existence of a state observer in terms of a linear matrix inequality. A numerical example is exploited to show the validity of the results obtained.

Sign in / Sign up

Export Citation Format

Share Document