DISCRETE-TIME MODEL-REDUCTION IN LIMITED FREQUENCY RANGES

A mathematical formulation for model reduction of discrete-time system s such that the reduced-order model represents the system in a particu lar frequency range is discussed. The algorithm transforms the full-or der system into balanced coordinates using frequency-weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is a ccomplished without need for numerical optimization. Balancing require s the computation of discrete frequency-weighted grammians. Closed-for m solutions for the computation of frequency-weighted grammians are de veloped. Numerical examples are discussed to demonstrate the algorithm .