D-stability analysis of polynomial matrices and polynomial matrix polytopes by using LMI approach

2012 ◽  
Author(s):  
Wang Feng ◽  
Xiong Pan ◽  
Chen Jian ◽  
Shi Li ◽  
Cao XiBin
Keyword(s):  
Stability Analysis ◽  
Polynomial Matrix ◽  
Lmi Approach ◽  
Polynomial Matrices

Neutral-type of delayed inertial neural networks and their stability analysis using the LMI Approach

2017 ◽  
Vol 230 ◽  
pp. 243-250 ◽  
Author(s):  
S. Lakshmanan ◽  
C.P. Lim ◽  
M. Prakash ◽  
S. Nahavandi ◽  
P. Balasubramaniam
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Neutral Type ◽  
Lmi Approach ◽  
Inertial Neural Networks

Algebraic Methods for the Construction of Algebraic-Difference Equations With Desired Behavior

2018 ◽  
Vol 34 ◽  
pp. 1-17 ◽  
Author(s):  
Lazaros Moysis ◽  
Nicholas Karampetakis
Keyword(s):  
Difference Equations ◽  
Polynomial Matrix ◽  
Elementary Divisor ◽  
System Of Equations ◽  
Polynomial Matrices ◽  
Linear System Of Equations ◽  
System A ◽  
Auto Regressive ◽  
Algebraic Difference ◽  
Forward Operator

For a given system of algebraic and difference equations, written as an Auto-Regressive (AR) representation $A(\sigma)\beta(k)=0$, where $\sigma $ denotes the shift forward operator and $A\left( \sigma \right) $ a regular polynomial matrix, the forward-backward behavior of this system can be constructed by using the finite and infinite elementary divisor structure of $A\left( \sigma \right) $. This work studies the inverse problem: Given a specific forward-backward behavior, find a family of regular or non-regular polynomial matrices $A\left( \sigma \right) $, such that the constructed system $A\left( \sigma \right) \beta \left( k\right) =0$ has exactly the prescribed behavior. It is proved that this problem can be reduced either to a linear system of equations problem or to an interpolation problem and an algorithm is proposed for constructing a system satisfying a given forward and/or backward behavior.

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