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Fernández-Anaya, G.; Martínez-García, J. C.; Kučera, V.

Characterizing families of positive real matrices by matrix substitutions on scalar rational functions. (English) Zbl 1113.93092

Syst. Control Lett. 55, No. 11, 871-878 (2006).
Summary: This paper concerns the characterization of positive real (PR) matrices generated by substitutions (of the Laplace variable \(s\)) in scalar rational transfer functions by matrix PR functions. Our main results are restricted to both strongly strictly PR matrices (SSPR) and strictly bounded real matrices. As a way to illustrate our main results, we also include here a partial extension of both the Kalman-Yakubovich-Popov lemma (for SSPR systems of zero relative degree) and the circle criterion (for strictly PR systems of zero relative degree).

Cited in 3 Documents

MSC:

93D20 Asymptotic stability in control theory
93B51 Design techniques (robust design, computer-aided design, etc.)
93C05 Linear systems in control theory
93B35 Sensitivity (robustness)

Keywords:

matrix positive real substitutions; properties preservation; linear time-invariant systems; robustness; Kalman-Yakubovich-Popov Lemma; circle criterion
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References:

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