On the Time-Weighted Quadratic Sum of Linear Discrete Systems
E.I. Jury, SHAUL GUTMAN · Journal of Dynamic Systems Measurement and Control · 1975
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.