Some Algorithmic Problems in Linear Systems I.
KENTUCKY UNIV LEXINGTON DEPT OF MATHEMATICS
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A comprehensive study of the stochastic realization problem was undertaken both in its algorithmic and structural aspects. A geometric state space theory of linear stochastic systems was obtained, providing a complete characterization of all stochastic realizations. The phenomenon of invariant directions of the matrix Riccati equation was investigated in this framework, clarifying its connections to filtering algorithms as well as to geometric aspects of linear systems theory. Non-Riccati algorithms for generating spectral factors were introduced. Work was initiated to develop a comprehensive framework for algorithms of this type through transformations in Hamiltonian systems. Author
- Statistics and Probability