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.
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