Exponential stabilization of time-varying delay systems with non-linear perturbations

2013 ◽  
Vol 31 (4) ◽  
pp. 441-464 ◽  
Author(s):  
M. V. Thuan ◽  
V. N. Phat ◽  
T. Fernando ◽  
H. Trinh
Keyword(s):  
Exponential Stabilization ◽  
Delay Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Linear Perturbations ◽  
Non Linear ◽  
Varying Delay

scholarly journals Input–output linearization of non-linear time-varying delay systems: the single-input single-output case

2019 ◽  
Vol 37 (3) ◽  
pp. 831-854
Author(s):  
Ihab Haidar ◽  
Florentina Nicolau ◽  
Jean-Pierre Barbot ◽  
Woihida Aggoune
Keyword(s):  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Input Output ◽  
Time Varying Delay ◽  
Output Stabilization ◽  
Non Linear ◽  
Varying Delay ◽  
Input Output Linearization

Abstract This paper deals with the input–output linearization of non-linear time-varying delay systems. We introduce an extension of the Lie derivative for time-varying delay systems and derive sufficient conditions for the existence of a causal and bounded non-linear feedback linearizing the input–output behaviour of the system. Sufficient conditions ensuring the internal stability after output stabilization are also presented. Finally, several examples illustrating our main results are discussed.

scholarly journals Exponential Stabilization of a Class of Time-Varying Delay Systems with Nonlinear Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Yazhou Tian ◽  
Yuanli Cai ◽  
Yuangong Sun ◽  
Tongxing Li
Keyword(s):  
Exponential Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Current State ◽  
Varying Delay ◽  
Reciprocally Convex Approach

This paper addresses the problem of exponential stabilization of a class of time-varying delay systems with nonlinear perturbations. These perturbations are related not only with current statextand the delayed statext−htbut also withβt, whereβtis a continuous function defined on[0,+∞). With the delay interval divided into two equidistant subintervals, a novel Lyapunov functional is introduced, and several new exponential stabilization criteria are derived in terms of linear matrix inequalities (LMIs) by employing reciprocally convex approach. Two examples are given to illustrate the effectiveness of the main results.

A novel sensor fault diagnosis approach for time-varying delay systems with non-linear uncertainty

2016 ◽  
Vol 39 (7) ◽  
pp. 1114-1120 ◽  
Author(s):  
Fuqiang You ◽  
Hui Li ◽  
Yingwei Zhang ◽  
Shouping Guan
Keyword(s):  
Fault Diagnosis ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Time Varying ◽  
Sensor Fault ◽  
Time Varying Delay ◽  
Non Linear ◽  
Diagnosis Algorithm ◽  
Varying Delay ◽  
Diagnosis Approach

In this paper, a sensor fault diagnosis approach is presented for a class of time delay non-linear systems via the use of adaptive updating rules. The considered system is represented by a time-varying delay dynamical state space model, and is subjected to a non-linear vector, which represents the modelling uncertainty in the state equation. Firstly, a fault detector observer is constructed to detect the fault. Then, the method for choosing the threshold value is given. Furthermore, a fault diagnosis device is constructed to diagnose the fault. The Lyapunov stability theory is used to obtain the required adaptive tuning rules for the estimation of the sensor fault. An adaptive diagnosis algorithm is developed to obtain information on the sensor fault. Finally, a simulated numerical example and a robotic example are included to demonstrate the use of the proposed approach, and experimental results show that the proposed adaptive diagnosis algorithm can track the fault signal and that the proposed method is valid.

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