On the asymptotic stability for a two-dimensional linear nonautonomous differential system

The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied.

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Asymptotic Stability and the Lyapunov Equation for Two-Dimensional Discrete Systems

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)60968-6 ◽

1984 ◽

Vol 17 (2) ◽

pp. 197-200

Author(s):

P. Agathoklis ◽

E.I. Jury ◽

M. Mansour

Keyword(s):

Asymptotic Stability ◽

Lyapunov Equation ◽

Discrete Systems ◽

Two Dimensional

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Asymptotic stability of two-dimensional continuous Roesser models with singularities at the stability boundary

2012 IEEE 51st IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc.2012.6426968 ◽

2012 ◽

Cited By ~ 2

Author(s):

Steffi Knorn ◽

Richard H. Middleton

Keyword(s):

Asymptotic Stability ◽

Stability Boundary ◽

Two Dimensional ◽

Roesser Models ◽

The Stability

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Parameter-dependent robust H∞ filtering for uncertain two-dimensional discrete systems in the FM second model

IMA Journal of Mathematical Control and Information ◽

10.1093/imamci/dnz039 ◽

2020 ◽

Vol 37 (4) ◽

pp. 1114-1132

Author(s):

Khalid Badie ◽

Mohammed Alfidi ◽

Mohamed Oubaidi ◽

Zakaria Chalh

Keyword(s):

Asymptotic Stability ◽

Lyapunov Function ◽

Discrete Systems ◽

Performance Criterion ◽

Linear Matrix ◽

Two Dimensional ◽

Matrix Inequalities ◽

Parameter Uncertainties ◽

Error System ◽

Parameter Dependent

Abstract This paper deals with the problem of robust $H_{\infty }$ filtering for uncertain two-dimensional discrete systems in the Fornasini–Marchesini second model with polytopic parameter uncertainties. Firstly, a new $H_{\infty }$ performance criterion is derived by exploiting a new structure of the parameter-dependent Lyapunov function. Secondly, based on the criterion obtained, a new condition for the existence of a robust $H_{\infty }$ filter that ensures asymptotic stability, and a prescribed $H_{\infty }$ performance level of the filtering error system, for all admissible uncertainties is established in terms of linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness and advantage of the proposed method.

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