2011
DOI: 10.3182/20110828-6-it-1002.02253
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On The Similarity State Transformation for Linear Parameter-Varying Systems

Abstract: Similarity state transformations between equivalent State-Space (SS) representations of discrete-time Linear Parameter-Varying (LPV) systems are investigated. Based on previous results, it is known that to characterize all equivalent LPV-SS representations, the statetransformation matrix must depend dynamically on the scheduling variable. However, preserving static dependence of a LPV-SS representation, i.e. characterizing all equivalent SS representation with static dependence, has primary importance both in … Show more

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Cited by 11 publications
(11 citation statements)
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“…It does not exclude other possible definitions, notably those based on p-dependent state transformation matrices T (p). Such considerations, related to LPV system equivalent state-space representations as investigated in [3], would be out of the scope of this technical communiqué. In practice, local LTI models are estimated from a finite data sample subject to random uncertainties, thus the definition of coherent local models is understood in an approximative sense.…”
Section: Definitionmentioning
confidence: 99%
“…It does not exclude other possible definitions, notably those based on p-dependent state transformation matrices T (p). Such considerations, related to LPV system equivalent state-space representations as investigated in [3], would be out of the scope of this technical communiqué. In practice, local LTI models are estimated from a finite data sample subject to random uncertainties, thus the definition of coherent local models is understood in an approximative sense.…”
Section: Definitionmentioning
confidence: 99%
“…However, as pointed out in [28], by applying a p-dependent linear transformation z(t) = T (p(t))x(t), the LPV system (1) becomes…”
Section: P-dependent Transformationsmentioning
confidence: 99%
“…Nevertheless, it has been reported in [28] that, in some particular case, there do exist p-dependent transformations preserving the static p-dependence of LPV models. How can this be possible?…”
Section: P-dependent Transformationsmentioning
confidence: 99%
“…It is important to note that TΣ ,Σ is not an LPV isomorphism between the two LPV models. In order for TΣ ,Σ to be an LPV isomorphism, A(p(t)) = TΣ ,Σ (p(t + 1))Â(p(t))T −1 Σ,Σ (p(t)), should hold for any scheduling signal p ∈ P, see Kulcsár and Tóth (2011); Tóth (2010) for more details.…”
Section: Preliminariesmentioning
confidence: 99%
“…As shown, e.g., in Tóth (2010); Lopes dos Santos et al (2011), existing techniques dedicated to the identification of Linear Parameter-Varying (LPV) systems can be split up into two main families: the local and the global approach. On the one hand, the global approach focuses on a global procedure for which it is assumed that one global experiment can be performed in which the control inputs as well as the scheduling variables can be both excited (see, e.g., Bamieh and Giarré (2002); Felici et al (2007)).…”
Section: Introductionmentioning
confidence: 99%