REALIZATION OF BILINEAR STOCHASTIC-SYSTEMS

The problem of realizing bilinear stochastic systems (BLSR) is analyzed. 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.