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W. Root (1975)
On the Modeling of Systems for Identification. I: $\varepsilon $-Representations of Classes of SystemsSiam Journal on Control, 13
WL Root (1975)
On the modeling of systems for identification. Part 1:ε-representations of classes of systemsSIAM J Control, 13
N Dunford, JT Schwartz (1958)
Linear operators, Part 1
W. Root (1977)
Considerations regarding input and output spaces for time-varying dynamical systemsApplied Mathematics and Optimization, 4
WA Porter (1978)
Approximation by Bernstein systemsMath Systems Theory, 11
R Saeks (1973)
Economics and Mathematical Systems 82
B. Rao, K. Parthasarathy (1967)
Probability measures on metric spaces
WL Root (1980)
Analysis and Optimisation of Stochastic Systems
R. Saeks (1973)
Resolution space; operators and systems
R. Saeks (1976)
Reproducing kernel resolution space and its applications—IIJournal of The Franklin Institute-engineering and Applied Mathematics, 302
W. Root (1975)
On the Modeling of Systems for Identification. Part II: Time-Varying SystemsSiam Journal on Control, 13
The notion of system trajectory of a time-varying input-output, dynamical system is reviewed. By introducing a probability measure on a class of such systems a stochastic system, the randomized system, is defined. The randomized system has a trajectory induced by the trajectories of the original systems. A theorem is proved giving fairly general conditions under which the randomized system trajectory is generated by a strongly continuous semigroup of bounded linear operators in a Banach space. An example is presented for a system represented by a quadratic integral operator.
Applied Mathematics and Optimization – Springer Journals
Published: Mar 26, 2005
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