Information theoretic methods for stochastic model reduction based on state projection

Based on state projection method with two-step operations, this paper deals with the model reduction problem by analyzing the information descriptions of system states. Our basic idea in obtaining the reduced-order models is to minimize the information loss or the conditional information loss caused by truncation by eliminating the state variables with the least contribution to system information. Before truncation, an entropy preserving transformation of the original state is required. The derived minimum information loss (MIL) and minimum conditional information loss (MCIL) methods are proved to be efficient for approximating stable and unstable systems, respectively, and connected with the balanced truncation methods firmly. Illustrative examples are given.