Calculation of Quadratic Moments of High-Order Linear Systems via Routh Canonical Transformation

In this paper, three different methods are developed for calculating various moments of the system variables of a linear system, represented by matrix equation x = Ax. A transformation Q is developed which transforms the system matrix A into a special matrix R. Liapunov function V is considered as V = x
_t
Q
_t
Qx and it facilitates evaluation of various moments ∫
₀
^∞
t
^m
x
²
dt These methods are especially useful for high-order systems. Examples are included to explain each method.