Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems. (English) Zbl 1224.93025

Reitmann, V.

Math. Bohem. 136, No. 2, 185-194 (2011).

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.

MSC:

93B15	Realizations from input-output data
93D25	Input-output approaches in control theory
93C80	Frequency-response methods in control theory
93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C25	Control/observation systems in abstract spaces

Keywords:

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