scholarly journals RobustH∞Control for Linear Stochastic Partial Differential Systems with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xisheng Dai ◽  
Feiqi Deng ◽  
Jianxiang Zhang
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Mean Square ◽  
Feedback Controllers ◽  
Partial Differential ◽  
Mean Square Exponential Stability ◽  
Linear Matrix Inequality Approach

This paper investigates the problems of robust stochastic mean square exponential stabilization and robustH∞for stochastic partial differential time delay systems. Sufficient conditions for the existence of state feedback controllers are proposed, which ensure mean square exponential stability of the resulting closed-loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level ofH∞performance. A linear matrix inequality approach is employed to design the desired state feedback controllers. An illustrative example is provided to show the usefulness of the proposed technique.

scholarly journals Memory State-Feedback Stabilization for a Class of Time-Delay Systems with a Type of Adaptive Strategy

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Lin Chai ◽  
Shumin Fei
Keyword(s):  
Time Delay ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Adaptive Strategy ◽  
Adaptive Controller ◽  
Feedback Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Memory State ◽  
Memory State Feedback

Stabilization of a class of systems with time delay is studied using adaptive control. With the help of the “error to error” technique and the separated “descriptor form” technique, the memory state-feedback controller is designed. The adaptive controller designed can guarantee asymptotical stability of the closed-loop system via a suitable Lyapunov-Krasovskii functional. Some sufficient conditions are derived for the stabilization together with the linear matrix inequality (LMI) design approach. Finally, the effectiveness of the proposed control design methodology is demonstrated in numerical simulations.

Sliding Mode H∞-Control with Stochastic Time Delay Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1712-1718
Author(s):  
Ravi Kumar ◽  
Kil To Chong
Keyword(s):  
Time Delay ◽  
Sliding Mode ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Linear Filter ◽  
Time Delay Systems ◽  
Stochastic Time

In this paper, we concerned the problem of sliding mode of-control with stochastic stabilization of uncertainty. Some sufficient conditions are derived for this class of robust feedback stabilization of time delay systems. The stochastic time delay systems may switch from one to one corresponds of linear filter, such that the dynamics of estimation error is guaranteed to be stochastically stable in mean square. Moreover, it is shown that for a class of special linear stochastic neutral systems, the H-sliding mode control design can be obtained by solving linear matrix inequalities (LMIs).

Further Results on Exponential Stability and State Feedback Stabilization for Time Delay Singular Saturating Actuator Systems With Delay-Dependence

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Time Delay ◽  
Convex Optimization ◽  
State Feedback ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Decision Variables ◽  
Delay Dependence

This paper will study the exponential stable and state feedback stabilization of time delay singular systems with saturation actuators. Some sufficient conditions for existence of controller are obtained by using the linear matrix inequalities (LMIs) and integral inequality approach (IIA). When these LMIs are feasible, an explicit expression of controller is obtained. Based on Lyapunov–Krasovskii functional (LKF) techniques, a novel exponential stabilization criterion has been also derived in terms of LMIs which can be easily solved with efficient convex optimization algorithm. Our results are less conservative than some existing ones, and the decision variables involved in this paper are less than them. Examples illustrate our results as less conservative than those reported in the literature.

State feedback observer-based control design for linear descriptor systems with multiple time-varying delays

2020 ◽  
Vol 37 (4) ◽  
pp. 1218-1236
Author(s):  
V N Phat ◽  
P Niamsup ◽  
N H Muoi
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Feedback Controllers ◽  
Delay Function ◽  
Delay Dependent

Abstract In this paper, we propose an linear matrix inequality (LMI)-based design method to observer-based control problem of linear descriptor systems with multiple time-varying delays. The delay function can be continuous and bounded but not necessarily differentiable. First, by introducing a new set of improved Lyapunov–Krasovskii functionals that avoid calculating the derivative of the delay function, we obtain new delay-dependent sufficient conditions for guaranteeing the system to be regular, impulse-free and asymptotically stable. Then, based on the derived stability conditions, we design state feedback controllers and observer gains via LMIs, which can be solved numerically in standard computational algorithms. A numerical example with simulation is given to demonstrate the efficiency and validity of the proposed deign.

scholarly journals Attractor and Boundedness of Switched Stochastic Cohen-Grossberg Neural Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Chuangxia Huang ◽  
Jie Cao ◽  
Peng Wang
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Mean Square ◽  
Ultimate Boundedness ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Uniformly Ultimate Boundedness

We address the problem of stochastic attractor and boundedness of a class of switched Cohen-Grossberg neural networks (CGNN) with discrete and infinitely distributed delays. With the help of stochastic analysis technology, the Lyapunov-Krasovskii functional method, linear matrix inequalities technique (LMI), and the average dwell time approach (ADT), some novel sufficient conditions regarding the issues of mean-square uniformly ultimate boundedness, the existence of a stochastic attractor, and the mean-square exponential stability for the switched Cohen-Grossberg neural networks are established. Finally, illustrative examples and their simulations are provided to illustrate the effectiveness of the proposed results.

scholarly journals Robust Exponential Stabilization of Uncertain Impulsive Bilinear Time-Delay Systems with Saturating Actuators

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Shujie ◽  
Shi Bao ◽  
Zhang Qiang ◽  
Pan Tetie
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Dynamics ◽  
Saturating Actuators ◽  
Robust Exponential Stabilization

This paper investigates the problem of robust exponential stabilization for uncertain impulsive bilinear time-delay systems with saturating actuators. By using the Lyapunov function and Razumikhin-type techniques, two classes of impulsive systems are considered: the systems with unstable discrete-time dynamics and the ones with stable discrete-time dynamics. Sufficient conditions for robust stabilization are obtained in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the theoretical results.

State Feedback Control for Fractional Differential Systems with Riemann-Liouville Derivative

2012 ◽  
Vol 562-564 ◽  
pp. 2053-2056
Author(s):  
Yuan Fang
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Liouville Derivative ◽  
Fractional Differential

This paper studies state feedback control for fractional differential systems with Riemann-Lιiouville derivative, which matrix A not satisfying the condition ιarg(λ(A))ι>α/2 . Based on the state feedback controllers’ designer, and Linear Matrix Inequality (LMI) apαproach, sufficient conditions for the systems with fraction order α (0<α<1) and α (1≤α<2) obtained respectively.

Design of State Feedback Controller for Discrete Systems with Time-Delay

2013 ◽  
Vol 347-350 ◽  
pp. 695-700
Author(s):  
Shuai Tian He ◽  
Zhi Chang Li
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
State Feedback ◽  
Controller Design ◽  
Dynamic Performance ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Adjustable Parameter ◽  
Linear Matrix ◽  
Feedback Gain

The stability analysis and controller design of discrete linear systems with time-varying delay are addressed. Firstly, the uniformly asymptotical stability criterion with adjustable parameter is derived by Lyapunov-Razumikhin approach. Then, the stabilization approaches for linear systems with time delay by state feedback and observer based-on state feedback are also presented. Sufficient conditions for the existence of state feedback gain and the observer gain are derived through the numerical solution of a set of obtained linear matrix inequalities. Compared with methods in the references, the dynamic performance of systems, such as the overshoot and the convergence rate of the response, can be adjusted by changing the adjustable parameter. Lastly, an illustrative example is given to show the effectiveness of the proposed.

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