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Js.lä:w I

275252951821

function Cab,

= bal real (a, b, c)
X BALREAL Balanced state-space realization and model reduction. X

= BALREAL(A,B,C) returns a balanced state-space X realization of the system (A, B, C).
X= also returns a vector

X containing the diagonal of the gramian of the balanced
X realization, and matrix T, the similarity transformation
X used to convert (A, B, C) to (Abs Cb) . If the system (A, B, C) X normalized properly, small elements In gramian m indicate
X states that can be removed to reduce the model to lower order.

x J.N. Little 3-6-86 x Copyright (c) 1986 by the MathWorks, Inc .

gram(a, b) ;X Compute the reachabillty gramian
155458112017

balanced
realization
cb
=
c*T;

balanced

realization

cb

=

در این سایت فقط تکه هایی از این مطلب با شماره بندی انتهای صفحه درج می شود که ممکن است هنگام انتقال از فایل ورد به داخل سایت کلمات به هم بریزد یا شکل ها درج نشود

شما می توانید تکه های دیگری از این مطلب را با جستجو در همین سایت بخوانید

ولی برای دانلود فایل اصلی با فرمت ورد حاوی تمامی قسمت ها با منابع کامل

اینجا کلیک کنید

c*T;

Go gram(a’ . c’ ) ; X Compute the observability gramian chol (Go) ;
X Make RGR exactly symmetric.
X Sort the diagonal elements of the gramian

Moore, B. , Principal Component Analysis in Linear Sys— tems: Control labi li ty, Observabili ty,and Model Reduction”
207278192042

IEEE TAC,

20 Luenberger, D, , Introduction to Dynamic Systems, Wiley,

1 979B
30 Kai lath, Ta ,

Prenti ce—Ha11 , 1980.
4-Gontmacher, Matrix Theory, Vol e l, Chelsea, 1977ø
14661877776187

13991263971922

13899813981066

50 Hammärling , n Numerical Sol ution of the Stable, Non—nega— ti ve Definite Lyapunov Equation”, IMA Journal of Numerical

Analysis,

60 MATLAB Software, The MATHWORKS Inc. , 21 Elliot Street, South

Natick, MA 01760, U.S.A.

Luenberger Optimization by Vector Space Methods, Wiley,

196%

Gl over , K. , “All Optimal Hanke1—Norm Approximation of Linear

Multi variable Systems and Their L00 Error Bounds”, Inter—

national Journal of Control g, Vol. 39, No, 6, pp. 1115—1193,

1984.

y 90

Laub A e, et,al, Computation of Balancing Transformations and Other Applications. of Simul taneous Diagonalization

TAC, Vol.32,pp.115-122i 1987.
10 e Vidyasagar, Control System Synthesis, M.I. T. Press, 1985,
11 p

Paliouras, Complex Variables for Scientists and Engineers,

Macmillan, 1975.

M. Safanov and Chiang, A Schur Method for Balanced— Truncation Model Reduction”, IEEE TAC, Vol .34 , No. 7,
July 1989,pp. 729-73.3


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