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Model Reduction of Discrete-Time Bilinear Second Order-Structured Systems in Infinite and Finite Frequency Intervals

In this paper, model order reduction techniques for discrete-time bilinear second order structured systems (SOSSs) over finite and infinite frequency intervals are proposed. Mathematical developments regarding generalized system form, system Gramians, Lyapunov equations and reduction mechanism for bilinear SOSSs for infinite and finite frequency intervals have been discussed. The formulation involves derivative pairs of each state and reduction techniques for such systems require retention of state pairs in a reduced order model to make reduction meaningful/useful. Retention of the state's structure has been achieved by partitioning the system Gramians into position and velocity portions. Balancing Gramians with different combinations yields different second-order balanced truncation techniques (SOBTs). The resulting SOBTs are tested on a bilinear system model for infinite and finite interval applications. Results certify for correct development as per claimed superiority of later proposed techniques in the limited intervals. The proposed developments can be considered for model order reduction of discrete-time bilinear second order structured system application especially over finite and infinite frequency intervals.