Robust Stability of Uncertain Switched Delay Systems with Nonlinear Perturbations

2011 ◽  
Vol 228-229 ◽  
pp. 782-788
Author(s):  
Chang Cheng Xiang ◽  
Xiu Liu ◽  
Xiu Yong Ding
Keyword(s):  
Robust Stability ◽  
Delay Differential Equations ◽  
Stability Problem ◽  
Delay Systems ◽  
Nonlinear Perturbations ◽  
Linear Delay ◽  
The Stability ◽  
Delay Differential ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper focuses on the stability problem of a class of uncertain switched delay systems with nonlinear perturbations. Applying multiple functional technique, we establish a delay dependent stability condition via designing appropriate switching rule. It should emphasize that this result is a standard extension of linear delay differential equations. Meanwhile, this result is presented by LMIs and thus solved easily.

scholarly journals Stability of delay differential equations in the sense of Ulam on unbounded intervals

2019 ◽  
Vol 9 (2) ◽  
pp. 125-131 ◽  
Author(s):  
Süleyman Öğrekçi
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Stability Problem ◽  
The Stability ◽  
Delay Differential ◽  
Unbounded Intervals

In this paper, we consider the stability problem of delay differential equations in the sense of Hyers-Ulam-Rassias. Recently this problem has been solved for bounded intervals, our result extends and improve the literature by obtaining stability in unbounded intervals. An illustrative example is also given to compare these results and visualize the improvement.

Stability of nonlinear time-delay systems satisfying a quadratic constraint

2016 ◽  
Vol 40 (3) ◽  
pp. 712-718 ◽  
Author(s):  
Mohsen Ekramian ◽  
Mohammad Ataei ◽  
Soroush Talebi
Keyword(s):  
Time Delay ◽  
Uncertain Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Quadratic Constraint ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities.

A Delay-Dividing Approach for Stability of Neutral System with Mixed Delays

2012 ◽  
Vol 468-471 ◽  
pp. 405-408
Author(s):  
Fang Qiu ◽  
Quan Xin Zhang
Keyword(s):  
Stability Problem ◽  
Lyapunov Functional ◽  
Mixed Delays ◽  
Neutral System ◽  
Stability Criteria ◽  
Numerical Examples ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper studies the stability problem for the neutral system with mixed delays. By constructing a novel Lyapunov functional based on a delay-dividing approach, some delay-dependent stability criteria are derived to guarantee the stability of the neutral system. It is established theoretically that the criteria are less conservative than recent reported ones. Two numerical examples are demonstrated to illustrate the effectiveness of the proposed results.

A New Look at the Stability Analysis of Delay-Differential Equations

2005 ◽  
Author(s):  
Tama´s Kalma´r-Nagy
Keyword(s):  
Difference Equation ◽  
Differential Equations ◽  
Characteristic Equation ◽  
Delay Differential Equations ◽  
Linear Delay ◽  
The Laplace Transform ◽  
Method Of Steps ◽  
The Difference ◽  
The Stability ◽  
Delay Differential

It is shown that the method of steps for linear delay-differential equations combined with the Laplace-transform can be used to determine the stability of the equation. The result of the method is an infinite dimensional difference equation whose stability corresponds to that of the transcendental characteristic equation. Truncations of this difference equation are used to construct numerical stability charts. The method is demonstrated on a first and second order delay equation. Correspondence between the transcendental characteristic equation and the difference equation is proved for the first order case.

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