Robust Absolute Stabilization of Time-Varying Delay Systems with Maximum Admissible Perturbed Bound

2010 ◽  
Vol 40-41 ◽  
pp. 103-110
Author(s):  
Jie Jin
Keyword(s):  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Law ◽  
Time Varying ◽  
Time Varying Delay ◽  
Linear State ◽  
Varying Delay ◽  
Nonlinear Delay

This paper is concerned the problem of robust absolute stabilization of time-varying delay systems with admissible perturbation in terms of integral inequality. A linear state-feedback control law is derived for one class of delay systems with sector restriction based on linear matrix inequality (LMI). Especially, this method does not require input terms are absolutely controllable for nonlinear delay systems. Numerical example is used to demonstrate the validity of the proposed method.

scholarly journals H∞Control for Nonlinear Systems with Time-Varying Delay Using Matrix-Based Quadratic Convex Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
C. Emharuethai ◽  
P. Niamsup
Keyword(s):  
Nonlinear System ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Time Varying Delay ◽  
Varying Delay

H∞control problem for nonlinear system with time-varying delay is considered by using a set of improved Lyapunov-Krasovskii functionals including some integral terms, and a matrix-based on quadratic convex, combined with Wirtinger's inequalities and some useful integral inequality.H∞controller is designed via memoryless state feedback control and new sufficient conditions for the existence of theH∞state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

State feedback stabilization of linear descriptor time-varying delay systems

2020 ◽  
Vol 42 (12) ◽  
pp. 2191-2197 ◽  
Author(s):  
Piyapong Niamsup ◽  
Vu N Phat
Keyword(s):  
State Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Descriptor Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Delay Function ◽  
Time Varying Delay ◽  
Varying Delay

In this paper, the augmented Lyapunov-Krasovskii function approach combining with singular value decomposition method is developed for stabilization of linear descriptor systems with time-varying delay. The delay function is non-differentiable, but continuous and bounded. By introducing a set of improved Lyapunov-Krasovskii functionals we propose delay-dependent sufficient conditions for admissibility of the system in terms of linear matrix inequalities. Then, based on the obtained stability results the problem of stabilization is solved via state feedback controllers, which guarantees that the descriptor closed-loop system is admissible. An numerical example with simulation is provided to show the effectiveness of the theoretical result.

State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay

2015 ◽  
Vol 82 (1-2) ◽  
pp. 349-355 ◽  
Author(s):  
Omar Naifar ◽  
Abdellatif Ben Makhlouf ◽  
Mohamed Ali Hammami ◽  
Abderrazak Ouali
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Control Law ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay

scholarly journals Time-Varying Delayed H∞ Control Problem for Nonlinear Systems: A Finite Time Study Using Quadratic Convex Approach

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 713 ◽  
Author(s):  
Chanikan Emharuethai ◽  
Piyapong Niamsup ◽  
Raja Ramachandran ◽  
Wajaree Weera
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

In this manuscript, we consider the finite-time H ∞ control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a H ∞ controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time H ∞ state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.

scholarly journals Finite-Time Stabilization of Switched Systems with Time-Varying Delay

2020 ◽  
pp. 24-31
Author(s):  
Mengxiao Deng ◽  
Yali Dong
Keyword(s):  
Feedback Control ◽  
Finite Time ◽  
State Feedback ◽  
State Feedback Control ◽  
Delay Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Finite Time Stabilization ◽  
Varying Delay ◽  
Event Triggered

This paper studies the problem of finite-time stabilization of a class of switched linear time-varying delay systems. An event-triggered sampling mechanism and an event-triggered state feedback control are proposed. Based on Lyapunov-like function method, linear matrix inequality technique and averaged dwell time method, sufficient conditions for switched delay systems under event-triggered state feedback control are given to ensure the finite-time stabilization of the switched delay systems. Finally, a numerical example is given to verify the validity of the proposed results.

Guaranteed Cost Control of Saturated Time-Varying Delay Systems

2012 ◽  
Vol 235 ◽  
pp. 129-134
Author(s):  
Han Lin He ◽  
Xiao Dong Wang ◽  
Wei Jun Li
Keyword(s):  
Schur Complement ◽  
Controller Synthesis ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Time Varying Delay ◽  
Guaranteed Cost ◽  
Degree Function ◽  
Varying Delay

This paper mainly considers the control problem of saturated time-varying delay systems. Applying the saturation degree function and the convex hull theory to handle the saturated terms, we put forward the guaranteed cost controller of the system according to the Lyapunov-Krasovskii theorem. Then we make use of Schur complement to convert the QMI (quadratic matrix inequality) to a LMI (linear matrix inequality) and so it can be easily used as controller synthesis. Finally, we apply the guaranteed cost controller to a two dimentional time-varying delay cellular neural networks, and the simulation results show the effectiveness of the proposed controller.

scholarly journals A Parametric Learning and Identification Based Robust Iterative Learning Control for Time Varying Delay Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Lun Zhai ◽  
Guohui Tian ◽  
Yan Li
Keyword(s):  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Multiple Input ◽  
And Performance ◽  
Varying Delay

A parametric learning based robust iterative learning control (ILC) scheme is applied to the time varying delay multiple-input and multiple-output (MIMO) linear systems. The convergence conditions are derived by using theH∞and linear matrix inequality (LMI) approaches, and the convergence speed is analyzed as well. A practical identification strategy is applied to optimize the learning laws and to improve the robustness and performance of the control system. Numerical simulations are illustrated to validate the above concepts.

scholarly journals Stability analysis for neural networks with discrete and leakage time-varying delay systems with delay-range-dependence and delay-derivative-dependence

2021 ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Neural Networks ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Decomposition Approach ◽  
Time Varying Delay ◽  
Systems Model ◽  
The Neural Networks ◽  
The Stability ◽  
Varying Delay

The paper deals with the stability problem of neural networks with discrete and leakage interval time-varying delays. Firstly, a novel Lyapunov-Krasovskii functional was constructed based on the neural networks leakage time-varying delay systems model. The delayed decomposition approach (DDA) and integral inequality techniques (IIA) were altogether employed, which can help to estimate the derivative of Lyapunov-Krasovskii functional and effectively extend the application area of the results. Secondly, by taking the lower and upper bounds of time-delays and their derivatives, a criterion on asymptotical was presented in terms of linear matrix inequality (LMI), which can be easily checked by resorting to LMI in Matlab Toolbox. Thirdly, the resulting criteria can be applied for the case when the delay derivative is lower and upper bounded, when the lower bound is unknown, and when no restrictions are cast upon the derivative characteristics. Finally, through numerical examples, the criteria will be compared with relative ones. The smaller delay upper bound was obtained by the criteria, which demonstrates that our stability criterion can reduce the conservatism more efficiently than those earlier ones.

Improved Results on Stability Criteria for Singular Systems with Interval Time-Varying Delays

2020 ◽  
pp. 2130001
Author(s):  
Chaibi Noreddine ◽  
Belamfedel Alaoui Sadek ◽  
Tissir El Houssaine ◽  
Bensalem Boukili
Keyword(s):  
Singular Systems ◽  
Singular System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Varying Delay ◽  
Singular Time

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results.

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