We consider differential-algebraic systems (DAEs) whose transfer function is outer: ., it has full row rank and all transmission zeros lie in the closed left half complex plane. We characterize outer, with the aid of the Kronecker structure of the system pencil and the Smith–McMillan structure of the transfer function, as the following property of a behavioural stabilizable and detectable realization: each consistent initial value can be asymptotically controlled to zero while the output can be made arbitrarily small in the -norm. The zero dynamics of systems with outer transfer functions are analyzed. We further show that our characterizations of outer provide a simple and very structured analysis of the linear-quadratic optimal control problem.
Accepté le :
DOI : 10.1051/cocv/2015051
Mots-clés : Differential-algebraic equations, outer transfer function, matrix pencils, zero dynamics, minimum phase, optimal control
@article{COCV_2017__23_2_391_0,
author = {Ilchmann, Achim and Reis, Timo},
title = {Outer transfer functions of differential-algebraic systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {391--425},
publisher = {EDP-Sciences},
volume = {23},
number = {2},
year = {2017},
doi = {10.1051/cocv/2015051},
zbl = {1358.93051},
mrnumber = {3608086},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2015051/}
}
TY - JOUR AU - Ilchmann, Achim AU - Reis, Timo TI - Outer transfer functions of differential-algebraic systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 391 EP - 425 VL - 23 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2015051/ DO - 10.1051/cocv/2015051 LA - en ID - COCV_2017__23_2_391_0 ER -
%0 Journal Article %A Ilchmann, Achim %A Reis, Timo %T Outer transfer functions of differential-algebraic systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 391-425 %V 23 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2015051/ %R 10.1051/cocv/2015051 %G en %F COCV_2017__23_2_391_0
Ilchmann, Achim; Reis, Timo. Outer transfer functions of differential-algebraic systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 391-425. doi : 10.1051/cocv/2015051. http://www.numdam.org/articles/10.1051/cocv/2015051/
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