Control-oriented properties preservation in linear systems when applying PR0 substitutions
| Authors: | Martinez-Garcia Juan Carlos, CINVESTAV-IPN, Mexico
Fernandez-Anaya Guillermo, Universidad Iberoamericana, Mexico
Kucera Vladimir, Czech Technical University, Czech Republic
Flores-Godoy Jose Job, Universidad Iberoamericana, Mexico |
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| Topic: | 2.5 Robust Control |
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| Session: | Fundamentals of Robust Control |
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| Keywords: | Linear time-invariant systems, robustness, positive real rational functions, stabilization, properties preservation. |
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Abstract
We present in this paper some results concerning the preservation of control-oriented properties in Linear Time-Invariant systems (LTI systems) when applying substitutions of the Laplace variable s by a particular class of positive real functions, the so-called Positive Real functions of zero relative degre (PR0 functions). In particular, we show that the families of Bounded Real (BR), Strictly Bounded Real (SBR), and Positive Real (PR), rational functions are closed under compositions with the specified class of positive real functions. We also give some results concerning the preservation of stability in proper real rational transfer functions (in fact this is our main result), as well as the preservation of the H-infinity-norm bound for this class of systems. Our study is restricted to Single-Input Single Output (SISO) systems.
