scholarly journals Full solution of random autonomous first-order linear systems of difference equations. Application to construct random phase portrait for planar systems

2017 ◽  
Vol 68 ◽  
pp. 150-156 ◽  
Author(s):  
J.-C. Cortés ◽  
A. Navarro-Quiles ◽  
J.-V. Romero ◽  
M.-D. Roselló
Keyword(s):  
Phase Portrait ◽  
Linear Systems ◽  
Difference Equations ◽  
Random Phase ◽  
Order Linear ◽  
First Order ◽  
Planar Systems ◽  
Full Solution

Observer–PID Stabilization Strategy for Unstable First-Order Linear Systems with Large Time Delay

2012 ◽  
Vol 51 (25) ◽  
pp. 8477-8487 ◽  
Author(s):  
J. F. Márquez-Rubio ◽  
B. del-Muro-Cuéllar ◽  
M. Velasco-Villa ◽  
D. F. Novella-Rodríguez
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Large Time ◽  
Order Linear ◽  
First Order

Stabilization strategy for unstable first order linear systems with large time-delay

2011 ◽  
Vol 14 (5) ◽  
pp. 1171-1179 ◽  
Author(s):  
J. F. Márquez-Rubio ◽  
B. del Muro-Cuéllar ◽  
M. Velasco-Villa ◽  
J. Álvarez-Ramírez
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Large Time ◽  
Order Linear ◽  
First Order

Stabilization Strategy for Unstable First Order Linear Systems with Large Time Delay

2010 ◽  
Vol 43 (21) ◽  
pp. 249-253
Author(s):  
B. del-Muro-Cuéllar ◽  
J.F. Márquez-Rubio ◽  
M. Velasco-Villa ◽  
J. Alvarez-Ramirez
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Large Time ◽  
Order Linear ◽  
First Order

Linear Stochastic Difference Equations

2013 ◽  
Author(s):  
Lars Peter Hansen ◽  
Thomas J. Sargent
Keyword(s):  
Time Series ◽  
Difference Equation ◽  
Difference Equations ◽  
Martingale Difference ◽  
Stochastic Difference Equation ◽  
Stochastic Difference Equations ◽  
Order Linear ◽  
Economic Agents ◽  
First Order ◽  
Competitive Equilibria

This chapter describes the vector first-order linear stochastic difference equation. It is first used to represent information flowing to economic agents, then again to represent competitive equilibria. The vector first-order linear stochastic difference equation is associated with a tidy theory of prediction and a host of procedures for econometric application. Ease of analysis has prompted the adoption of economic specifications that cause competitive equilibria to have representations as vector first-order linear stochastic difference equations. Because it expresses next period's vector of state variables as a linear function of this period's state vector and a vector of random disturbances, a vector first-order vector stochastic difference equation is recursive. Disturbances that form a “martingale difference sequence” are basic building blocks used to construct time series. Martingale difference sequences are easy to forecast, a fact that delivers convenient recursive formulas for optimal predictions of time series.

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