On the theory of realization of quasilinear systems described by differential equations in a Hilbert space

We consider a system-theoretic methodology of mathematical modeling involved in the structural identification of continuous nonlinear dynamic systems with programmable position control. We present various functional-analytical modifications of a characteristic criterion for exogenous (“input-output”) behavior of these systems that permit, by virtue of this criterion, model realizations in the class of quasilinear nonstationary ordinary differential equations describing states in a separable Hilbert space. The study was sponsored by the Russian Foundation for Basic Research (Grant No. 05-01-00623), Basic Research Program No. 22 of the Presidium of the Russian Academy of Sciences, Grant of the President of the Russian Federation for the Governmental Support of Scientific Schools of the Russian Federation (No. NSh-1676.2008). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 82–95, September–October 2008.