Frequency Interval Cross Gramians for Linear and Bilinear Systems

Ahmad Jazlan, Victor Sreeram, Hamid Reza Shaker, Roberto Togneri, Ha Binh Minh

    Research output: Contribution to journalArticlepeer-review

    18 Citations (Scopus)


    In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians relative to existing methods.

    Original languageEnglish
    Pages (from-to)22-34
    Number of pages13
    JournalAsian Journal of Control
    Issue number1
    Publication statusPublished - 1 Jan 2017


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