Existence and Asymptotic Stability of Periodic Two-Dimensional Contrast Structures in the Problem with Weak Linear Advection

2019 ◽  
Vol 106 (5-6) ◽  
pp. 771-783
Author(s):  
N. N. Nefedov ◽  
E. I. Nikulin
Keyword(s):  
Asymptotic Stability ◽  
Two Dimensional ◽  
Contrast Structures

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

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.

scholarly journals Exact stability and instability regions for two-dimensional linear autonomous multi-order systems of fractional-order differential equations

2021 ◽  
Vol 24 (1) ◽  
pp. 225-253
Author(s):  
Oana Brandibur ◽  
Eva Kaslik
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fractional Order ◽  
Autonomous Systems ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Fractional Order Differential Equations ◽  
Stability And Instability ◽  
Instability Regions ◽  
Necessary And Sufficient

Abstract Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and fractional-order-independent stability and instability properties are fully characterised, in terms of the main diagonal elements of the systems’ matrix, as well as its determinant.

scholarly journals On the Boussinesq Equations with Non-monotone Temperature Profiles

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
Christian Zillinger
Keyword(s):  
Asymptotic Stability ◽  
Couette Flow ◽  
Nonlinear Equations ◽  
Boussinesq Equations ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Partial Dissipation ◽  
Suitable Norm ◽  
Rayleigh Benard

AbstractIn this article, we consider the asymptotic stability of the two-dimensional Boussinesq equations with partial dissipation near a combination of Couette flow and temperature profiles T(y). As a first main result, we show that if $$T'$$ T ′ is of size at most $$\nu ^{1/3}$$ ν 1 / 3 in a suitable norm, then the linearized Boussinesq equations with only vertical dissipation of the velocity but not of the temperature are stable. Thus, mixing enhanced dissipation can suppress Rayleigh–Bénard instability in this linearized case. We further show that these results extend to the (forced) nonlinear equations with vertical dissipation in both temperature and velocity.

scholarly journals On the stability of 2D general Roesser Lyapunov systems

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 85-97
Author(s):  
Mohammed Amine Ghezzar ◽  
Djillali Bouagada ◽  
Kamel Benyettou ◽  
Mohammed Chadli ◽  
Paul Van Dooren
Keyword(s):  
Asymptotic Stability ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
The Stability

This paper addresses the problem of stability for general two-dimensional (2D) discrete-time and continuous-discrete time Lyapunov systems, where the linear matrix inequalities (LMI's) approach is applied to derive a new sufficient condition for the asymptotic stability.

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