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A Relative Error Bound for Discrete Balanced Stochastic Truncation

The relative-error of discrete time Balanced Stochastic Truncation (BST) model reduction is derived. Fundamental differences between discrete-time BST and its continuous-time counterpart are shown to preclude a straightforward application of bilinear mappings to directly generalize existing continuous-time error bounds. Nevertheless, a crude L¿ relative error bound for discrete time multi-input multi-output system BST model reduction is derived. It is hope that the preliminary results reported here will lay the foundation for a simpler, tighter error bound for discrete time BST.