Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control

Hartmut Logemann; Ruth F. Curtain

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 5, page 395-424
  • ISSN: 1292-8119

Abstract

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We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator and the nonlinearity ϕ satisfies a sector condition of the form (ϕ(u),ϕ(u) - au) ≤ 0 for some constant a>0. These results are used to prove convergence and stability properties of low-gain integral feedback control applied to exponentially stable, linear, well-posed systems subject to actuator nonlinearities. The class of actuator nonlinearities under consideration contains standard nonlinearities which are important in control engineering such as saturation and deadzone.

How to cite

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Logemann, Hartmut, and Curtain, Ruth F.. "Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 395-424. <http://eudml.org/doc/116566>.

@article{Logemann2010,
abstract = { We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator and the nonlinearity ϕ satisfies a sector condition of the form (ϕ(u),ϕ(u) - au) ≤ 0 for some constant a>0. These results are used to prove convergence and stability properties of low-gain integral feedback control applied to exponentially stable, linear, well-posed systems subject to actuator nonlinearities. The class of actuator nonlinearities under consideration contains standard nonlinearities which are important in control engineering such as saturation and deadzone. },
author = {Logemann, Hartmut, Curtain, Ruth F.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Absolute stability; actuator nonlinearities; circle criterion; integral control; positive real; robust tracking; well-posed infinite-dimensional systems.; well-posed linear systems; absolute stability; circle criterion},
language = {eng},
month = {3},
pages = {395-424},
publisher = {EDP Sciences},
title = {Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control},
url = {http://eudml.org/doc/116566},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Logemann, Hartmut
AU - Curtain, Ruth F.
TI - Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 395
EP - 424
AB - We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator and the nonlinearity ϕ satisfies a sector condition of the form (ϕ(u),ϕ(u) - au) ≤ 0 for some constant a>0. These results are used to prove convergence and stability properties of low-gain integral feedback control applied to exponentially stable, linear, well-posed systems subject to actuator nonlinearities. The class of actuator nonlinearities under consideration contains standard nonlinearities which are important in control engineering such as saturation and deadzone.
LA - eng
KW - Absolute stability; actuator nonlinearities; circle criterion; integral control; positive real; robust tracking; well-posed infinite-dimensional systems.; well-posed linear systems; absolute stability; circle criterion
UR - http://eudml.org/doc/116566
ER -

References

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