Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems

In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying dominant subspaces based reachability Gramian a system. Once desired subspace computed, reduced order then obtained Galerkin projection. We prove that, in case, either preserves mean square asymptotic stability or leads to models whose minimal realization asymptotically stable. This preservation guarantees existence system which basis error bounds that we derive. bound depends neglected eigenvalues hence shows these values are good indicator expected dimension procedure. Subsequently, establish result systems similar manner. These latter results recently proved link between conclude paper numerical experiments using benchmark problem. compare with balanced truncation show it performs well reproducing