# 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

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topLogemann, 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 -

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