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# MICHALETZKY, Gy. - BOKOR, J. - VÁRLAKI, P.: Representability of stochastic systems
The purpose of this book is to investigate modeling
and representation approaches of stationary stochastic phenomena. These
approaches have their origins in the theory ofmultivariate stochastic processes,
time series analysis and in the algebraic geometric theory of stochastic
systems. The stochastic representations most frequently used are the
auto-regressive-moving-average (ARMA), matrix-fraction-descriptions
(MFD) and the state-space representations. It is shown how to derive these
- forward a nd backward - representations and their dual forms from
the analytic and co-analytic spectral factors. These representations are
parametrized by system invariants reflecting the four basic
Kalmanian principles of controllability, observability,
reachabil ity and reconstructibility. Detailed structure of the state-space
realizations is provided using geometric (Hilbert-space) principles including
the analysis of the zero structure and balanced realizations. The structure
of generalized Wiener-Hopf factorization is studied in details, first using geometric consideration, then computing the system
matrices. The perspective provided by this can be interesting for those
who are doing research in signal processing, stochastic modeling and system
identification, or in control system design. Parts of the text can also
be useful in courses on stochastic systems.
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