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Lossless Systems Storage Function: New Results and Numerically Stable and Non-Iterative Computational Methods

Kothyari, A., Praagman, C. & Belur, M. N., Dec-2018, In : IEEE Transactions on Circuits and Systems I - Regular papers. 65, 12, p. 4349 - 4362 24 p.

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In this paper, we formulate and prove new results in the context of storage functions for lossless systems: we use these results to propose new algorithms to compute the storage function. The computation of the storage function for the lossless case is not possible using conventional algebraic Riccati equation-based algorithms, though the storage function itself is well-defined. This is because a certain “regularity condition” on the feedthrough term in the i/s/o representation of the lossless system does not hold. We formulate new results about the storage function matrix for the lossless case and use them to propose non-iterative and stable algorithms to compute the storage function directly from different representations of the given system, namely, a kernel representation, transfer function, and the i/s/o representation of the system. Across the methods, for randomly generated transfer functions, we compare: 1) the computational effort (in flops); 2) the computation time using numerical experiments; and 3) the computational error.
Original languageEnglish
Pages (from-to)4349 - 4362
Number of pages24
JournalIEEE Transactions on Circuits and Systems I - Regular papers
Volume65
Issue number12
Publication statusPublished - Dec-2018

    Keywords

  • Transfer functions , Kernel , Riccati equations , Springs , Resistance , Transmission line matrix methods , Indexes, Algebraic Riccati equation (ARE), subspace intersection algorithms, Zassenhaus algorithm, QUADRATIC DIFFERENTIAL FORMS

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