By L Dugard; M MʼSaad; Yoan D Landau; International Federation of Automatic Control
Adaptive structures stay a really attention-grabbing box of theoretical learn, prolonged through methodological reports and more and more purposes. The plenary papers, invited classes and contributed periods fascinated with many points of adaptive platforms, reminiscent of platforms id and modelling, adaptive regulate of nonlinear platforms and theoretical matters in adaptive regulate. additionally lined have been methodological points and purposes of adaptive keep an eye on, clever tuning and adaptive sign processing.
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Extra info for Adaptive systems in control and signal processing 1992 : selected papers from the fourth IFAC symposium, Grenoble, France, 1-3 July 1992
Collecting all these facts, we get the proposition D of Lemma 1 . We make the conclusion of Lemma 1 slightly stronger, stating simply that v• is to be a real linear space con taining all constants (in other words, we "complete" the rational linear space). A practical question is how to de fine this space. It is known from theory of linear spaces (Kolmogorov and Fomin, 1970) that any real linear sub space of codimension n can be expressed as the intersec tion of kernels (null spaces) of n linear functionals, say L; .
2) as constant symmetric diagonal positive definite matrix, P is a symmetric positive definite matrix satisfying 'l'T p + P'lf = -Q, Q .. ). 4A) Q (2. 1 ) and parameter error system . = Amax(R) I (coAmin( P)) • �= Amin(R)/(c1Amax(P)), B4=-C6Amax(R)/(c1Amax(P)) Tlreorem I. W WT®(VijF)®W. W where ® is Kronecker product operator. 6) l. 3) This condition ( named persistent excitation ) allows X and cp both converge exponentially to zero. 3) is not satisfied the system is u. s. +oo, the limits X -+0, cp -+ some constant vector.
6) l. 3) This condition ( named persistent excitation ) allows X and cp both converge exponentially to zero. 3) is not satisfied the system is u. s. +oo, the limits X -+0, cp -+ some constant vector. 7) Theorem (i) is well known proved by Narendra  and omited here. s. matrix. system (3. 2) is u. a. s. in a sufficiently small neighborhood of the origin. > II -+0 implies " II G(t)X II I II X II tends to zero with II X II -+O''. From ( 3 . > II + 8 4 the following Lyapunov equation of the system gives Q () � 2o ' l with � = Amin(R) I (c1Amax(P)), 8 4 = - C6 Amax(R) I (c1Amax(P)) .
Adaptive systems in control and signal processing 1992 : selected papers from the fourth IFAC symposium, Grenoble, France, 1-3 July 1992 by L Dugard; M MʼSaad; Yoan D Landau; International Federation of Automatic Control