By Cornelius T. Leondes
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Additional resources for Advances in Theory and Applications : System Identification and Adaptive Control, Part 2
The mapping from K(z) into τ : -»- Θ C R d : K(z) G U + τ ψ = Φ (K(z)) G Θ . , , and further extended by several authors  and Result U proved (see, ). 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 ) .
21a) y(n) = "i · o o x(n) . o : o lj This equation is equivalent to the one in (17). We remark that a number of random sequences are generated to drive the system. All results are surprisingly identical. The obtained transfer matrix is also exact; no numerical error is introduced in the computation. 25 -1 Π 0 1. u(n) , x(n) . 749 - z is obtained. 2zJ The result is again exact. This confirms that the algorithm used is a numerically stable one. More simula tions for systems with higher degrees are under way.
G (nxs) £ G. Δ 1 = (n±xs) 'ill J lln. isn. ], ID (nxn) i, j = 1, with -a. ~ M. ) 1 1 n3 -a. 1 -a . n n ..
Advances in Theory and Applications : System Identification and Adaptive Control, Part 2 by Cornelius T. Leondes