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Article

Reitmann, Volker
Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems. (English). Mathematica Bohemica, vol. 136 (2011), issue 2, pp. 185-194
MSC: 34B16, 34C25, 45D05, 47G10, 47H14, 93B15, 93D10 | MR 2856135 | Zbl 1224.93025 | DOI: 10.21136/MB.2011.141581
Keywords:
infinite dimensional Volterra integral equation; realization theory; absolute instability; frequency-domain method
Summary:
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.
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