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Typically mathematical models of physical and chemical processes are large and complex because of complications and nonlinearities of physical processes. The importance of mathematical models is evident for optimization and control purposes. Large rigorous mathematical models are cause of high computational loads and computational times, restricting the use of such models for online applications. This provides the opportunity to use reduced models, which are match of NL processes within defined 'operational domain' which can achieve low computational loads and faster simulation times.

Block structured models (in particular Hammerstein structure) have been used for identification purposes efficiently, but have not been used for model reduction purposes. Block structured models have advantage in approximation and identification; the approximated or identified block structures give insight to the complex and complicated process, hence providing handle for reduction. In this study, input-state (IS) Hammerstein block structure is used for the approximation and model reduction of NL process. Initially input-output Hammerstein block structure has been used for approximation (identification) of NL process. The methodology has been extended to IS Hammerstein structure. In this work, it is shown that I/S Hammerstein structure can be derived by Taylor series expansion (under trivial assumptions). Mathematically, I/S Hammerstein structure is given (as in equation below) and is shown in Fig. (1);