Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems

Ruth F Curtain, Mark R Opmeer

Research output: Contribution to journalArticle

3 Citations (Scopus)
86 Downloads (Pure)

Abstract

We solve the problem of robust stabilization with respect to right-coprime factor perturbations for irrational discrete-time transfer functions. The key condition is that the associated dynamical system and its dual should satisfy a finite-cost condition so that two optimal cost operators exist. We obtain explicit state space formulas for a robustly stabilizing controller in terms of these optimal cost operators and the generating operators of the realization. Along the way we also obtain state space formulas for Bezout factors.
Original languageEnglish
Pages (from-to)101-115
Number of pages15
JournalMathematics of Control Signals and Systems
Volume23
Issue number1-3
DOIs
Publication statusPublished - 2011

Fingerprint

Coprime Factorization
Robust Stabilization
Infinite-dimensional Systems
Discrete-time Systems
Factorization
Stabilization
State Space
Costs
Operator
Coprime
Transfer Function
Transfer functions
Dynamical systems
Discrete-time
Dynamical system
Perturbation
Controller
Controllers

Cite this

Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems. / Curtain, Ruth F; Opmeer, Mark R.

In: Mathematics of Control Signals and Systems, Vol. 23, No. 1-3, 2011, p. 101-115.

Research output: Contribution to journalArticle

@article{8a095c1316bf43318f464a129ec139e9,
title = "Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems",
abstract = "We solve the problem of robust stabilization with respect to right-coprime factor perturbations for irrational discrete-time transfer functions. The key condition is that the associated dynamical system and its dual should satisfy a finite-cost condition so that two optimal cost operators exist. We obtain explicit state space formulas for a robustly stabilizing controller in terms of these optimal cost operators and the generating operators of the realization. Along the way we also obtain state space formulas for Bezout factors.",
author = "Curtain, {Ruth F} and Opmeer, {Mark R}",
year = "2011",
doi = "10.1007/s00498-011-0068-5",
language = "English",
volume = "23",
pages = "101--115",
journal = "Mathematics of Control Signals and Systems",
issn = "0932-4194",
publisher = "Springer London",
number = "1-3",

}

TY - JOUR

T1 - Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems

AU - Curtain, Ruth F

AU - Opmeer, Mark R

PY - 2011

Y1 - 2011

N2 - We solve the problem of robust stabilization with respect to right-coprime factor perturbations for irrational discrete-time transfer functions. The key condition is that the associated dynamical system and its dual should satisfy a finite-cost condition so that two optimal cost operators exist. We obtain explicit state space formulas for a robustly stabilizing controller in terms of these optimal cost operators and the generating operators of the realization. Along the way we also obtain state space formulas for Bezout factors.

AB - We solve the problem of robust stabilization with respect to right-coprime factor perturbations for irrational discrete-time transfer functions. The key condition is that the associated dynamical system and its dual should satisfy a finite-cost condition so that two optimal cost operators exist. We obtain explicit state space formulas for a robustly stabilizing controller in terms of these optimal cost operators and the generating operators of the realization. Along the way we also obtain state space formulas for Bezout factors.

UR - http://www.scopus.com/inward/record.url?scp=83555166289&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/s00498-011-0068-5

U2 - 10.1007/s00498-011-0068-5

DO - 10.1007/s00498-011-0068-5

M3 - Article

VL - 23

SP - 101

EP - 115

JO - Mathematics of Control Signals and Systems

JF - Mathematics of Control Signals and Systems

SN - 0932-4194

IS - 1-3

ER -