On the Time-Weighted Quadratic Sum of Linear Discrete Systems

[+] Author and Article Information
E. I. Jury

Department of Electrical Engineering and Computer Sciences and the Electronics Research Laboratory, University of California, Berkeley, Calif.

S. Gutman

Department of Mechanical Engineering, University of California, Berkeley, Calif.

J. Dyn. Sys., Meas., Control 97(4), 441-444 (Dec 01, 1975) (4 pages) doi:10.1115/1.3426962 History: Received June 02, 1975; Online July 13, 2010


In this paper the weighted quadratic sum

J = k=0∞ xk1 Qk xk
of a stable linear discrete system xk+1 = Axk is discussed. The formula of J is obtained from matrix z-transform formulation. Alternatively, it is shown that the weighted sum index J can be calculated recursively from a matrix equation. Finally, a combinatorial rule is obtained for calculating this matrix equation.

Copyright © 1975 by ASME
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