On the issue of finding of the Lyapunov matrix for a class of linear system with delay

2018 ◽  
Author(s):  
Mikhail Chashnikov
Keyword(s):  
Linear System ◽  
System With Delay ◽  
Lyapunov Matrix

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

scholarly journals Stabilisation of Discrete-Time Piecewise Homogeneous Markov Jump Linear System with Imperfect Transition Probabilities

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Ding Zhai ◽  
Liwei An ◽  
Jinghao Li ◽  
Qingling Zhang
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Feedback Controller ◽  
Sufficient Condition ◽  
Markov Jump ◽  
Stochastically Stable ◽  
Lyapunov Matrix ◽  
The Stability ◽  
Markov Jump Linear System

This paper is devoted to investigating the stability and stabilisation problems for discrete-time piecewise homogeneous Markov jump linear system with imperfect transition probabilities. A sufficient condition is derived to ensure the considered system to be stochastically stable. Moreover, the corresponding sufficient condition on the existence of a mode-dependent and variation-dependent state feedback controller is derived to guarantee the stochastic stability of the closed-loop system, and a new method is further proposed to design a static output feedback controller by introducing additional slack matrix variables to eliminate the equation constraint on Lyapunov matrix. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed methods.

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.

Sign in / Sign up

Export Citation Format

Share Document