On the Time-Weighted Quadratic Sum of Linear Discrete Systems
- 1 December 1975
- journal article
- Published by ASME International in Journal of Dynamic Systems, Measurement, and Control
- Vol. 97 (4) , 441-444
- https://doi.org/10.1115/1.3426962
Abstract
In this paper the weighted quadratic sum J=∑k=0∞xk1Qkxk 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.Keywords
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