Time- and frequency-limited H 2-optimal model order reduction of bilinear control systems

Umair Zulfiqar, Victor Sreeram, Mian Ilyas Ahmad, Xin Du

Research output: Contribution to journalArticlepeer-review


In the time- and frequency-limited model order reduction, a reduced-order approximation of the original high-order model is sought to ensure superior accuracy in some desired time and frequency intervals. We first consider the time-limited (Formula presented.) -optimal model order reduction problem for bilinear control systems and derive first-order optimality conditions that a local optimum reduced-order model should satisfy. We then propose a heuristic algorithm that generates a reduced-order model, which tends to achieve these optimality conditions. The frequency-limited and the time-limited (Formula presented.) -pseudo-optimal model reduction problems are also considered wherein we restrict our focus on constructing a reduced-order model that satisfies a subset of the respective optimality conditions for the local optimum. Two new algorithms have been proposed that enforce two out of four optimality conditions on the reduced-order model upon convergence. The algorithms are tested on three numerical examples to validate the theoretical results presented in the paper. The numerical results confirm the efficacy of the proposed algorithms.

Original languageEnglish
Pages (from-to)1953-1973
Number of pages21
JournalInternational Journal of Systems Science
Issue number10
Early online date28 Jan 2021
Publication statusPublished - 2021


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