Approximation of stochastic systems: Reduced-order estimator & controller

A new algorithm for reducing continuous-time stochastic systems is presented. First, using the theory of canonical variables and the canonical decomposition of the Hankel operator a new algorithm for obtaining balanced stochastic realization (BSR) is developed. Next, using the insight obtained from this result a direct approach for obtaining BSR is presented. Model reduction is achieved by picking an appropriate subsystem of the BSR. Asymptotic stability of the reduced-order model, as well as the inverse of the reduced-order model is established. This leads to a new design for reduced-order Kalman-Bucy filters. Finally the spectral domain interpretations of the BSR are given. Also a reduced order controller for the LQR problem is developed.