Geodesic
Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems
Mathematica Bohemica, Tome 136 (2011) no. 2, pp. 185-194.

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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.
DOI : 10.21136/MB.2011.141581
Classification : 34B16, 34C25, 45D05, 47G10, 47H14, 93B15, 93D10
Keywords: infinite dimensional Volterra integral equation; realization theory; absolute instability; frequency-domain method 
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Reitmann, Volker. Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems. Mathematica Bohemica, Tome 136 (2011) no. 2, pp. 185-194. doi : 10.21136/MB.2011.141581. http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141581/

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