scholarly journals Stability of Uncertain 2-D Discrete Systems in Presence of Generalized Overflow Nonlinearities

2019 ◽  
Vol 8 (6S3) ◽  
pp. 725-732
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Nonlinear Effects ◽  
Discrete Systems ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Roesser Model ◽  
Discontinuous Systems ◽  
Reciprocally Convex Approach

Stability analysis of two-dimensional (2-D) discontinuous systems with generalized overflow nonlinear effects is considered in this work. The 2-D models considered are the well-known Fornasini Marchesini Second Local State-Space (FMSLSS) model and the Roesser model. The effect of uncertainties and interim-like variable time-delays on the system is also examined in the study. Using reciprocally convex approach we provide stability criteria which is organized as matrix inequalities. Numerical illustrations are given to demonstrate the applicability of the results.

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 On Stability Analysis for Generalized Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Generalized Neural Networks

This paper deals with the problem of stability analysis for generalized neural networks with time-varying delays. With a suitable Lyapunov-Krasovskii functional (LKF) and Wirtinger-based integral inequality, sufficient conditions for guaranteeing the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). By applying the proposed methods to two numerical examples which have been utilized in many works for checking the conservatism of stability criteria, it is shown that the obtained results are significantly improved comparing with the previous ones published in other literature.

scholarly journals Robust Stability Criteria of Roesser-Type Discrete-Time Two-Dimensional Systems with Parameter Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yan Zhao ◽  
Tieyan Zhang ◽  
Dan Zhao ◽  
Fucai You ◽  
Miao Li
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
2D Systems ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Parameter Dependent

This paper is concerned with robust stability analysis of uncertain Roesser-type discrete-time two-dimensional (2D) systems. In particular, the underlying parameter uncertainties of system parameter matrices are assumed to belong to a convex bounded uncertain domain, which usually is named as the so-called polytopic uncertainty and appears typically in most practical systems. Robust stability criteria are proposed for verifying the robust asymptotical stability of the related uncertain Roesser-type discrete-time 2D systems in terms of linear matrix inequalities. Indeed, a parameter-dependent Lyapunov function is applied in the proof of our main result and thus the obtained robust stability criteria are less conservative than the existing ones. Finally, the effectiveness and applicability of the proposed approach are demonstrated by means of some numerical experiments.

scholarly journals Stability analysis of linear neutral systems with multiple time delays

2005 ◽  
Vol 2005 (2) ◽  
pp. 175-183 ◽  
Author(s):  
Keyue Zhang
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Spectral Radius ◽  
Time Delays ◽  
Multiple Time ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Numerical Examples ◽  
Multiple Time Delays ◽  
New Criteria

This paper studies the asymptotic stability of linear neutral systems with multiple time delays. Using the characteristic equation of the system, new delay-independent stability criteria are derived in terms of the spectral radius of modulus matrices. Numerical examples are given to demonstrate the validity of our new criteria.

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