By E. Walter
It's the aim of technology to formalize the relationships among saw amounts. The motivations of this type of modelling strategy are diverse, yet can rougnly be amassed round pOles. If one is worried with approach keep an eye on, one desires to discover a version which wl11 De aDle to predlct tne method Denavlor, taKlng lnto account tne applled lnputs. The version will then be evaluated on it5 skill to imitate the ob5e ved input-output habit below c: onditione; ae; vari"d ae; po
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Additional info for Identifiability of State Space Models: with applications to transformation systems
Example text
The 0i are the nonzero singular values, the number of which is equal to the rank of M. In practice some of the singular values which theoretically would be zero may happen to be small but nonzero. iu\:: wIJIl;1J ~Inyular values are taken as zero. Tecnnlques ot numerlcal analysiS are now available to estimate fairly precisely the number of 3ignificant digits of a nu- merical result. ~n hp rli~tinOlli~hprl from 2pro. takina into account the precision of the computer used [VI 1 . One of the interesting properties of the singular-value decomposition, in addition to its great numerical stability, comes from the very concrete meaning of tne nonzero slngular values.
OlloJi Lioll. Q~ The point to stress is that easily operated algorithms exist which enable structural observability and structural controllability of linear models to be checked in so far as the nonzero entries of the matrices A, Band C are free parameters. unfortunately tnls IS not always tne case. 5) or when a class does not have any flow to the outside, forcing the sum of the entries of the corresponding column of A to be zero. It is thus necessary to design "ad hoc" methods which account for the possible unobservability or uncontrollability resulting trom tne relatlonsnlps eXlstlng oetween parameters.
However this can be extremely expensive even for rather simple examples. >t. 4 MAIN APPROACI~S TO STRUCTURAL IDCNTlrIAOILITY Before examining the various methods available in the literature for checking structural identifiability, we first present two modelling approaches that avoHI the problem. rlbuLlulI~ clfnl 1I111ILdllulI::'. 3) are said to be equivalent if, and only if, there exists a state-space similarity transformation which changes one into the other. A set of construction rules makes it possible to associate a unique (canonical) representat10n w1th any equIvalence class (or orbIt).