Small-gain theorem and finite-frequency analysis of TCP/AQM system with time varying delay

2019 ◽  
Vol 13 (13) ◽  
pp. 1971-1982 ◽  
Author(s):  
Belamfedel Alaoui Sadek ◽  
Tissir El Houssaine ◽  
Chaibi Noreddine
Keyword(s):  
Frequency Analysis ◽  
Time Varying ◽  
Finite Frequency ◽  
Time Varying Delay ◽  
Small Gain Theorem ◽  
Small Gain ◽  
Varying Delay

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.

Robust sliding mode preview control for uncertain discrete-time systems with time-varying delay

2021 ◽  
pp. 095965182110553
Author(s):  
Junchao Ren ◽  
Changbin Jiang
Keyword(s):  
Sliding Mode ◽  
Reference Signal ◽  
Time Varying ◽  
Preview Control ◽  
Delayed Systems ◽  
Time Varying Delay ◽  
Sliding Motion ◽  
Small Gain ◽  
Time Systems ◽  
Varying Delay

This article focuses on the problem of robust sliding mode preview control for a class of non-linear delayed systems. It is assumed that the reference signal is previewed with a fixed length ahead and the norm of uncertainty is bounded. A model transformation is introduced to approximate the time-varying delay such that augmented error systems can be constructed. Conditions of asymptotic stability of sliding motion are established via the small gain theorem. The sliding mode preview controller is designed such that the controlled system state can be attracted to the switching surface and keep on it thereafter. A numerical example is presented to illustrate the effectiveness of the proposed control design.

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