scholarly journals Stabilization of a Class of Stochastic Systems with Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jian Wang ◽  
Cuixia Li
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Time Delays ◽  
Stochastic Systems ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Decomposition Technique ◽  
Stability Criteria ◽  
Stochastic Time

The problem of exponential stability is investigated for a class of stochastic time-delay systems. By using the decomposition technique and Lyapunov stability theory, two improved exponential stability criteria are derived. Finally, a numerical example is given to illustrate the effectiveness and the benefit of the proposed method.

Passive Control for Uncertain Stochastic Time-Delay Systems

2011 ◽  
Vol 58-60 ◽  
pp. 691-696
Author(s):  
Cheng Wang ◽  
Huan Bin Liu
Keyword(s):  
Time Delay ◽  
Passive Control ◽  
Stochastic Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
And Control ◽  
Stochastic Time

This paper investigates the problems of delay-dependent passive analysis and control for uncertain stochastic systems with time-varying delay and norm-bounded parameters uncertainties. Delay-dependent stochastic passive condition for the uncertain stochastic time-delay systems is obtained based on Laypunov-Krasovkii functional approach. On the basis of this condition, a delay-dependent passive controller is presented. Sufficient condition for the existence of desired controller is formulated in terms of linear matrix inequality. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

scholarly journals T-S Fuzzy Model-Based Approximation and Filter Design for Stochastic Time-Delay Systems with Hankel Norm Criterion

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yanhui Li ◽  
Xiujie Zhou
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Fuzzy Model ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Hankel Norm ◽  
Error System ◽  
Stochastic Time

This paper investigates the Hankel norm filter design problem for stochastic time-delay systems, which are represented by Takagi-Sugeno (T-S) fuzzy model. Motivated by the parallel distributed compensation (PDC) technique, a novel filtering error system is established. The objective is to design a suitable filter that guarantees the corresponding filtering error system to be mean-square asymptotically stable and to have a specified Hankel norm performance levelγ. Based on the Lyapunov stability theory and the Itô differential rule, the Hankel norm criterion is first established by adopting the integral inequality method, which can make some useful efforts in reducing conservativeness. The Hankel norm filtering problem is casted into a convex optimization problem with a convex linearization approach, which expresses all the conditions for the existence of admissible Hankel norm filter as standard linear matrix inequalities (LMIs). The effectiveness of the proposed method is demonstrated via a numerical example.

scholarly journals RobustH∞Filtering for General Nonlinear Stochastic State-Delayed Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Weihai Zhang ◽  
Gang Feng ◽  
Qinghua Li
Keyword(s):  
Time Delay ◽  
Stochastic Systems ◽  
Type Equation ◽  
State Equation ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Delayed Systems ◽  
Bounded Real Lemma ◽  
Stochastic Time

This paper studies the robustH∞filtering problem of nonlinear stochastic systems with time delay appearing in state equation, measurement, and controlled output, where the state is governed by a stochastic Itô-type equation. Based on a nonlinear stochastic bounded real lemma and an exponential estimate formula, an exponential (asymptotic) mean squareH∞filtering design of nonlinear stochastic time-delay systems is presented via solving a Hamilton-Jacobi inequality. As one corollary, for linear stochastic time-delay systems, a Luenberger-type filter is obtained by solving a linear matrix inequality. Two simulation examples are finally given to show the effectiveness of our results.

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