For a linear continuous-time control system in Hilbert space with state x(t) is associated a discrete-time system where the state variable is z k = (x((k + 1)h) + x(kh))/2, with small h. This allows to introduce a discrete derivative ∆z k = (x((k + 1)h) − x(kh))/h. The obtained discrete-time system has structural properties with a similar formulation as continuous sys-tem. Stability is equivalent to the fact that the spectrum of the state oper-ator of discrete-time system is in the left half plane, Lyapunov and Riccati equation are similar.
Publié le : 2001-07-04
Classification:
infinite dimensional systems,
discrete systems,
linear control systems,
[SPI.AUTO]Engineering Sciences [physics]/Automatic,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC],
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
@article{hal-01110295,
author = {Rabah, Rabah and Bergeon, Benoit},
title = {On state space representation for linear discrete-time systems in Hilbert spaces},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01110295}
}
Rabah, Rabah; Bergeon, Benoit. On state space representation for linear discrete-time systems in Hilbert spaces. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-01110295/