# Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems

Mathematica Bohemica (2011)

- Volume: 136, Issue: 2, page 185-194
- ISSN: 0862-7959

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topReitmann, Volker. "Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems." Mathematica Bohemica 136.2 (2011): 185-194. <http://eudml.org/doc/197211>.

@article{Reitmann2011,

abstract = {Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.},

author = {Reitmann, Volker},

journal = {Mathematica Bohemica},

keywords = {infinite dimensional Volterra integral equation; realization theory; absolute instability; frequency-domain method; infinite dimensional Volterra integral equation; realization theory; absolute instability; frequency-domain method},

language = {eng},

number = {2},

pages = {185-194},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems},

url = {http://eudml.org/doc/197211},

volume = {136},

year = {2011},

}

TY - JOUR

AU - Reitmann, Volker

TI - Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems

JO - Mathematica Bohemica

PY - 2011

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 136

IS - 2

SP - 185

EP - 194

AB - Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.

LA - eng

KW - infinite dimensional Volterra integral equation; realization theory; absolute instability; frequency-domain method; infinite dimensional Volterra integral equation; realization theory; absolute instability; frequency-domain method

UR - http://eudml.org/doc/197211

ER -

## References

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- Yakubovich, V. A., Frequency-domain conditions for stability of nonlinear integral equations of control theory, Vestn. Leningr. Univ. 7 (1967), 109-125 Russian. (1967)

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