By J. Schoukens

This booklet concentrates at the challenge of exact modeling of linear platforms. It offers a radical description of a mode of modeling a linear dynamic invariant method through its move functionality. the 1st chapters supply a common creation and assessment for these readers who're surprising with identity conception in order that they have a enough history wisdom for figuring out the tools defined later. the most physique of the e-book appears to be like on the simple strategy utilized by the authors to estimate the parameter of the move functionality, the way it is feasible to optimize the excitation indications. extra chapters expand the estimation process proposed. functions are then mentioned and the ebook concludes with sensible instructions which illustrate the tactic and supply a few rules-of-thumb.

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**Sample text**

H o w e v e r , if the matrix of the s e c o n d order derivative o n the right h a n d s i d e is not positive definite, there is n o g u a r a n t e e that the e x p r e s s i o n will b e negative, a n d the p r o c e d u r e can diverge. Only if the cost f u n a i o n is differentiable a n d the m i n i m u m is not a multiple solution (the H e s s i a n matrix is not singular) will it b e certain that the s e c o n d order derivatives will b e positive definite in the n e i g h b o r h o o d of the solution.

H o w e v e r , care is n e c e s s a r y if the main interest is in a physical inter pretation of the identification results, a s difference e q u a t i o n s are only a p p r o x i m a tions o f differential e q u a t i o n s inside a limited frequency b a n d . T h e a l l o w e d m a x i m a l frequency is only a small fraction of the S h a n n o n frequency. This will b e illustrated in the following e x a m p l e .

37) it can b e c o n c l u d e d that the MLE o f σ is the s q u a r e root of the estimated variance : —I ν 1=1 ΙΟΕΝΤηΠΟΑΉΟΝ OF UNEAR SYSTEMS 26 Conclusion It is clear from the p r e c e d i n g list that the m a x i m u m likelihood estimator p o s s e s s e s all of the properties w h i c h are required for a n ideal estimator, but only asymptoti cally with the n u m b e r of m e a s u r e m e n t s . Therefore the n u m b e r of m e a s u r e m e n t s s h o u l d b e large. B e c a u s e o f these properties, the m a x i m u m likelihood estimator has b e c o m e very p o p u l a r .