Frequency-Limited Model Reduction for Positive Systems


During this paper, the problem of frequency-restricted $mmb H_infty $ model reduction for positive linear time-invariant systems is investigated. Specifically, our goal is to find a stable positive reduced-order model for a given positive system such that the $mmb H_infty $ norm of the error system is bounded over a frequency interval of interest. A replacement condition in terms of matrix inequality is developed for characterizing the frequency-restricted $mmb H_infty $ performance. Then constant parametrization of a positive reduced-order model springs, primarily based on that, an iterative algorithm is built for optimizing the reduced-order model. The algorithm utilizes coarse reduced-order models ensuing from (generalized) balanced truncation because the initial value. Each continuous- and discrete-time systems are considered in the identical framework. Numerical examples clearly show the effectiveness and advantages of the proposed model reduction technique.

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