Realization of Bilinear Stochastic Systems

This paper considers the problem of realization of bilinear stochastic systems. First an explicit statement for the BLSR problem is presented. Next a realization algorithm is developed. In this algorithm the state vector is picked as a basis in the subspace obtained by projecting an appropriately defined past vector onto an appropriately defined future vector. Also the realization algorithm involves solving a matrix nonlinear equation which is akin to the algebraic Riccati equation except for one additional term.