scholarly journals Stabilization of time-delay systems with a Controlled time-varying delay and applications

2005 ◽  
Vol 50 (4) ◽  
pp. 493-504 ◽  
Author(s):  
W. Michiels ◽  
V. Van Assche ◽  
S.-I. Niculescu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Time Varying Delay ◽  
Varying Delay

scholarly journals Robustl2-l∞Filtering for Discrete-Time Delay Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chengming Yang ◽  
Zhandong Yu ◽  
Pinchao Wang ◽  
Zhen Yu ◽  
Hamid Reza Karimi ◽  
...  
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Estimation Error ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Time Varying Delay ◽  
Discrete Time Delay ◽  
Error System ◽  
Varying Delay

The problem of robustl2-l∞filtering for discrete-time system with interval time-varying delay and uncertainty is investigated, where the time delay and uncertainty considered are varying in a given interval and norm-bounded, respectively. The filtering problem based on thel2-l∞performance is to design a filter such that the filtering error system is asymptotically stable with minimizing the peak value of the estimation error for all possible bounded energy disturbances. Firstly, sufficientl2-l∞performance analysis condition is established in terms of linear matrix inequalities (LMIs) for discrete-time delay systems by utilizing reciprocally convex approach. Then a less conservative result is obtained by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, the robustl2-l∞filter is designed for systems with time-varying delay and uncertainty. Finally, a numerical example is given to demonstrate the effectiveness of the filter design method.

A new approach for the optimal control of time-varying delay systems with external persistent matched disturbances

2017 ◽  
Vol 24 (19) ◽  
pp. 4505-4512 ◽  
Author(s):  
Amin Jajarmi ◽  
Mojtaba Hajipour ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Necessary Optimality Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Augmented System ◽  
Varying Delay

The aim of this study is to develop an efficient iterative approach for solving a class of time-delay optimal control problems with time-varying delay and external persistent disturbances. By using the internal model principle, the original time-delay model with disturbance is first converted into an augmented system without any disturbance. Then, we select a quadratic performance index for the augmented system to form an undisturbed time-delay optimal control problem. The necessary optimality conditions are then derived in terms of a two-point boundary value problem involving advance and delay arguments. Finally, a fast iterative algorithm is designed for the latter advance-delay boundary value problem. The convergence of the new iterative technique is also investigated. Numerical simulations verify that the proposed approach is efficient and provides satisfactory results.

Exponential Delay Dependent Stabilization for Time-Varying Delay Systems With Saturating Actuator

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Time Delay ◽  
Design Method ◽  
Delay System ◽  
Rate Of Change ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

This paper deals with the stabilization criteria for a class of time-varying delay systems with saturating actuator. Based on the Lyapunov–Krasovskii functional combining with linear matrix inequality techniques and Leibniz–Newton formula, delay-dependent stabilization criteria are derived using a state feedback controller. We also consider efficient convex optimization algorithms to the time-varying delay system with saturating actuator case: the maximal bound on the time delay such that the prescribed level of operation range and imposed exponential stability requirements are still preserved. The value of the time-delay as well as its rate of change are taken into account in the design method presented and further permit us to reduce the conservativeness of the approach. The results have been illustrated by given numerical examples. These results are shown to be less conservative than those reported in the literature.

scholarly journals Further Stability Analysis of Time-Delay Systems with Nonlinear Perturbations

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Jie Sun ◽  
Jing Zhang
Keyword(s):  
Stability Analysis ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Double Integral ◽  
Time Varying Delay ◽  
Integral Forms ◽  
Varying Delay

In this study, we focus on stability analysis for systems with time-varying delay and nonlinear perturbations. In order to cut down the conservatism of the existing stability criteria, we utilize the triple integral forms of Lyapunov-Krasovskii functional (LKF). In addition, by using single and double integral forms of Wirtinger-based inequality, we overcome some conservatism which come from Jensen’s inequality. Three well-known numerical examples are given at the end. Compared with some existing results, our results have less conservatism.

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