Download Advances in Theory and Applications : System Identification by Cornelius T. Leondes PDF

By Cornelius T. Leondes

ISBN-10: 0120127261

ISBN-13: 9780120127269

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Extra resources for Advances in Theory and Applications : System Identification and Adaptive Control, Part 2

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G. GOODWIN and R. L. PAYNE, "Dynamic System Identification," Academic Press, New York, 19 77. 34 CHI-TSONG CHEN 4. R. K. MEHRA and D. G. LAINIOTIS, "System Identification: Advances and Case Studies," Academic Press, New York, 1976. 5. D. GRAUPE, "Identification and Adaptive Filtering," Krieger, Malabar, Florida, 1984. 6. T. C. HSIA, "Identification: Least Square Methods," Lex­ ington Books, Lexington, Massachusetts, 1977. 7. C. T. Chen, "Linear System Theory and Design," Holt, New York, 1984. 8.

48 MICHAEL GEVERS AND VINCENT WERTZ Definition 1. e(t)J into a unique output process y(t). Therefore (1), (9), (13), and (17) are all models by our definition, provided that specific values (rational functions or real-valued parameters or polynomials) are put into the oper­ ators G(z), H(z), A, B, C, K, ... , (10)]. We can therefore introduce the following definition. Definition 2. Let M and M be two models relating an input vector Tu _e to an output vector y, and let {G ( 1 ) (z) , Η ^ (z) } and {G^ 2) (z) , H (2) (z)} be the corresponding transfer functions.

S; I = 1, . , n i (36) where k-(i, j) is the shall call φ φ : U (i, j)th element of the matrix K-. the mapping from K(z) into τ : -»- Θ C R d : K(z) G U + τ ψ = Φ (K(z)) G Θ . , [2], and further extended by several authors [14] and Result U proved (see, [19]). 2. (1) S(n) is a real analytic manifold of dimension n(p + s ) . (2) S(n) is the union of the U is open and dense in S ( n ) ; Θ (3) φ described in (4) S(n) Δ U Comment 1. i < n such that |μ| = n. Each is open and dense in R . (37) is a homeomorphism between U an open and dense subset Θ of R , with d = n(p + s ) : Θ S(i) = Ü if and = Φ (U ) .

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