scholarly journals RobustH∞Control of Uncertain T-S Fuzzy Time-Delay System: A Delay Decomposition Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Cheng Gong ◽  
Chunsong Han
Keyword(s):  
Time Delay ◽  
Delay System ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Decomposition Approach ◽  
System A ◽  
Delay Decomposition Approach ◽  
Uncertain Time ◽  
Delay Dependent ◽  
Delay Decomposition

This paper is concerned with the problem of robustH∞control for a class of uncertain time-delay fuzzy systems with norm-bounded parameter uncertainties. By utilizing the instrumental idea of delay decomposition, the decomposed Lyapunov-Krasovskii functional is introduced to uncertain T-S fuzzy system, and some delay-dependent conditions for the existence of robust controller are formulated in the form of linear matrix inequalities (LMIs). When these LMIs are feasible, a controller is presented. A numerical example is given to demonstrate the effectiveness of the proposed method.

Delay-Dependent H∞ Filtering for Neural Networks with Time Delay

2014 ◽  
Vol 511-512 ◽  
pp. 875-879 ◽  
Author(s):  
Ya Jun Li ◽  
Yan Nong Liang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Filter Design ◽  
Linear Matrix ◽  
Globally Asymptotically Stable ◽  
H Infinity ◽  
Decomposition Approach ◽  
Delay Decomposition Approach ◽  
Error System ◽  
Delay Dependent

The H{infinity} filter design problem of recurrent neural networks with time delay is considered. Based on delay decomposition approach, the delay-dependent condition is derived to ensure that the filtering error system is globally asymptotically stable with a guaranteed performance. And the design of such a filter can be solved by the linear matrix inequality. A numerical example is provided to demonstrate that the developed approach is efficient.

Parameterization approach to stability and feedback stabilization of linear time-delay systems

2009 ◽  
Vol 223 (7) ◽  
pp. 929-939
Author(s):  
M S Mahmoud ◽  
A Ismail ◽  
F M Al-Sunni
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Delay System ◽  
Feedback Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Systematic Analysis ◽  
Feedback Scheme ◽  
Delay Dependent

This paper develops a new parameterized approach to the problems of delay-dependent analysis and feedback stabilization for a class of linear continuous-time systems with time-varying delays. An appropriate Lyapunov-Krasovskii functional is constructed to exhibit the delay-dependent dynamics. The construction guarantees avoiding bounding methods and effectively deploying injecting parametrized variables to facilitate systematic analysis. Delay-dependent stability provides a characterization of linear matrix inequalities (LMIs)-based conditions under which the linear time-delay system is asymptotically stable with a γ-level £2 gain. By delay-dependent stabilization, a state-feedback scheme is designed to guarantee that the closed-loop switched system enjoys the delay-dependent asymptotic stability with a prescribed γ-level £2 gain. It is established that the methodology provides the least conservatism in comparison with other published methods. Extension to systems with convex-bounded parameter uncertainties in all system matrices is also provided. All the developed results are tested on representative examples.

scholarly journals RobustH∞Control of Neutral System with Time-Delay for Dynamic Positioning Ships

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Dawei Zhao ◽  
Fuguang Ding ◽  
Lili Zhou ◽  
Wenying Zhang ◽  
He Xu
Keyword(s):  
Time Delay ◽  
Wind Waves ◽  
Delay System ◽  
Linear Matrix ◽  
Dynamic Positioning ◽  
Neutral System ◽  
Decomposition Approach ◽  
Delay Decomposition Approach ◽  
Conservative Result ◽  
System With Time Delay

Due to the input time-delay existing in most thrust systems of the ships, the robustH∞controller is designed for the ship dynamic positioning (DP) system with time-delay. The input delay system is turned to a neutral time-delay system by a state-derivative control law. The less conservative result is derived for the neutral system with state-derivative feedback by the delay-decomposition approach and linear matrix inequality (LMI). Finally, the numerical simulations demonstrate the asymptotic stability and robustness of the controller and verify that the designed DP controller is effective in the varying environment disturbances of wind, waves, and ocean currents.

scholarly journals A New Integral Inequality and Delay-Decomposition with Uncertain Parameter Approach to the Stability Analysis of Time-Delay Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Haiyang Zhang ◽  
Lianglin Xiong ◽  
Qing Miao ◽  
Yanmeng Wang ◽  
Chen Peng
Keyword(s):  
Time Delay ◽  
Integral Inequality ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Decomposition Approach ◽  
Delay Decomposition Approach ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Delay Decomposition

This paper is concerned with the problem of delay-dependent stability of time-delay systems. Firstly, it introduces a new useful integral inequality which has been proved to be less conservative than the previous inequalities. Next, the inequality combines delay-decomposition approach with uncertain parameters applied to time-delay systems, based on the new Lyapunov-Krasovskii functionals and new stability criteria for system with time-delay have been derived and expressed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness and the less conservative feature of the proposed method compared with some recent results.

scholarly journals Observer-based robust H∞, control for uncertain time-delay systems

2003 ◽  
Vol 44 (4) ◽  
pp. 625-634 ◽  
Author(s):  
Xinping Guan ◽  
Yichang Liu ◽  
Cailian Chen ◽  
Peng Shi
Keyword(s):  
Time Delay ◽  
Uncertain System ◽  
Delay System ◽  
Disturbance Attenuation ◽  
Delay Systems ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Parameter Uncertainties ◽  
Time Delay System ◽  
Uncertain Time

AbstractIn this paper, we present a method for the construction of a robust observer-based H∞ controller for an uncertain time-delay system. Cases of both single and multiple delays are considered. The parameter uncertainties are time-varying and norm-bounded. Observer and controller are designed to be such that the uncertain system is stable and a disturbance attenuation is guaranteed, regardless of the uncertainties. It has been shown that the above problem can be solved in terms of two linear matrix inequalities (LMIs). Finally, an illustrative example is given to show the effectiveness of the proposed techniques.

scholarly journals Robust Stability of Neutral System with Mixed Time-Varying Delays and Nonlinear Perturbations Using Delay Decomposition Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Fang Qiu ◽  
Quanxin Zhang
Keyword(s):  
Linear Matrix ◽  
Mixed Delays ◽  
Neutral System ◽  
The Novel ◽  
Nonlinear Perturbations ◽  
Decomposition Approach ◽  
Delay Decomposition Approach ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Delay Decomposition

This paper investigates the robust delay-dependent stability problem for neutral system with mixed delays and nonlinear perturbations. A delay decomposition approach is used in this paper in which the information of the delayed plant states can be taken into full consideration. Then, based on a special Lyapunov functional approach, the novel delay-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). A numerical example illustrates the effectiveness of the derived method and the improvement over some existing methods.

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.

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