Canonical correlations of past inputs and future outputs for linear stochastic systems
The paper deals with the dependence of future outputs on past inputs via canonical correlation analysis. One considers here a discrete-time stochastic system described by the state difference equation \(x(t+1)=Ax(t)+Bu(t)\) and the output equation \(y(t)=Cx(t)+Du(t)\) where A, B, C and D are constant matrices and the input u(t) is a normalized p- dimensional Gaussian white-noise. The author takes advantage of the fact that the usual notions of dependence between Gaussian processes can be reduced to geometric conditions which in turn can be expressed in terms of canonical correlation coefficients to focus on the characterization of these coefficients by means of system-theoretic quantities. Finally, the author indicates, how her results can be applied to the problem of approximating stochastic systems through lower-dimensional systems.
scientific article; zbMATH DE number 3869134
scientific article