Exponential estimate of the degree of damping and overregulation for a linear system with delay

2013 ◽  
Vol 13 (11) ◽  
Author(s):  
Artur Gorbunov
Keyword(s):  
Linear System ◽  
Exponential Estimate ◽  
System With Delay

On Closure of a Submodule and a Linear System with Delay

2001 ◽  
Vol 34 (13) ◽  
pp. 461-464
Author(s):  
Sri Wahyuni ◽  
Indah Emilia Wijayanti
Keyword(s):  
Linear System ◽  
System With Delay

Parametric identification of linear systems using AutoRegressive with eXogenous input model expansion on Meixner-like orthonormal bases

2019 ◽  
Vol 42 (2) ◽  
pp. 306-321
Author(s):  
Safa Maraoui ◽  
Kais Bouzrara
Keyword(s):  
Genetic Algorithms ◽  
Linear System ◽  
Linear Systems ◽  
Experimental Research ◽  
Parametric Identification ◽  
New Model ◽  
System With Delay ◽  
Orthonormal Bases ◽  
Bounded Error ◽  
Input Model

This paper proposes a new model for a representation of linear system with delay. This latter, is given by decomposing the coefficients of the AutoRegressive with eXogenous input (ARX) model associated with the output and the input on two independent Meixner-like orthonormal bases. The resulting model is called ARX Meixner-like model. In order to ensure the parameter complexity reduction, the Meixner-like poles are optimized using Genetic algorithms method. Unknown But Bounded Error (UBBE) approaches are used to update the uncertainty domain of the parameters of the new obtained model. A numerical example of system with delay and two examples of experimental research are made to prove the efficiency of the proposed approach.

scholarly journals Exponential Stability of Linear Discrete Systems with Multiple Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
J. Baštinec ◽  
H. Demchenko ◽  
J. Diblík ◽  
D. Ya. Khusainov
Keyword(s):  
Linear System ◽  
Exponential Stability ◽  
Difference Equations ◽  
Lyapunov Method ◽  
Discrete Systems ◽  
Exponential Estimate ◽  
Multiple Delays ◽  
System Of Difference Equations ◽  
New Criterion ◽  
Linear Discrete Systems

The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with multiple delays xk+1=Axk+∑i=1sBixk-mi, k=0,1,…, where s∈N, A and Bi are square matrices, and mi∈N. New criterion for exponential stability is proved by the Lyapunov method. An estimate of the norm of solutions is given as well and relations to the well-known results are discussed.

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