scholarly journals Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Zhixiong Zhong ◽  
Guanghui Sun ◽  
Hamid Reza Karimi ◽  
Jianbin Qiu
Keyword(s):  
Stability Analysis ◽  
Original System ◽  
Transformation Method ◽  
Delta Operator ◽  
Time Varying ◽  
Input Output ◽  
Time Varying Delay ◽  
Operator Systems ◽  
Delta Operator Systems ◽  
Varying Delay

The stability analysis and stabilization of Takagi-Sugeno (T-S) fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG) theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF) in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.

scholarly journals Stabilization of Delta Operator Systems with Actuator Saturation via an Anti-Windup Compensator

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1084 ◽  
Author(s):  
Hafsaa Rachid ◽  
Ouarda Lamrabet ◽  
El Houssaine Tissir
Keyword(s):  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Domain Of Attraction ◽  
Original System ◽  
Linear Matrix ◽  
Delta Operator ◽  
Time Varying Delay ◽  
Operator Systems ◽  
Small Gain ◽  
Delta Operator Systems

The design of an anti-windup controller for delta operator systems with time-varying delay and actuator saturation is addressed. By utilizing the input-output approach and three-term approximation, we first transform the original system into two equivalent interconnected subsystems. Then, by employing the scaled small-gain theorem, the Lyapunov–Krasovskii functional, and Wirtinger’s integral inequality, sufficient conditions for the synthesis of an anti-windup compensator are presented in the form of linear matrix inequalities (LMIs). The estimated domain of attraction is maximized by an optimization algorithm. Numerical examples are studied to show the merits of the proposed technique.

Delay-distribution-dependent Robust Stability Analysis of Uncertain Lurie Systems with Time-varying Delay

2012 ◽  
Vol 38 (7) ◽  
pp. 1100 ◽  
Author(s):  
Pankaj MUKHIJA ◽  
Indra Narayan KAR ◽  
Rajendra Kumar Purus BHATT
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Time Varying ◽  
Delay Distribution ◽  
Time Varying Delay ◽  
Robust Stability Analysis ◽  
Varying Delay

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

Stability analysis of piecewise linear delta operator systems

2008 ◽  
Author(s):  
Xu Yong ◽  
Li Jie ◽  
Tang Wansheng ◽  
Zhang Jianxiong ◽  
Wei Jie
Keyword(s):  
Stability Analysis ◽  
Piecewise Linear ◽  
Delta Operator ◽  
Operator Systems ◽  
Delta Operator Systems
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