Necessary and sufficient conditions for strictly positive real matrices

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Necessary and sufficient conditions for strictly positive real matrices

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In this paper we present some useful properties of strictly positive real transfer matrices for both continuous and discrete-time linear time-invariant systems in the frequency and state space domains. Some of these properties follow from known results and are presented for the sake of completeness. The new results obtained are mainly for discrete-time systems and include the discretetime version of the Lefschetz-Kalman-Yakubovich lemma for transfer matrices.

Inspec keywords: matrix algebra; frequency-domain synthesis; discrete time systems; state-space methods; transfer functions

Other keywords: Lefschetz-Kalman-Yakubovich lemma; discrete-time version; discrete-time linear time-invariant systems; frequency domain; control systems; continuous linear time-invariant system; state space domains; positive real transfer matrices

Subjects: Discrete control systems; Control system analysis and synthesis methods; Algebra

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