Hamzi - Eurandom

Balancing of Linear Control Systems
• Typically one looks for a gap in the singular values {σi} for guidance as
to where truncation should occur. If we see that there is a k such that
σk ≫ σk+1, then the states most responsible for governing the
input-output relationship of the system are (x1, · · · , xk) while
(xk+1, . . . , xn) are assumed to make negligible contributions.
• Although several methods exist for computing T , the general idea is to
compute the Cholesky decomposition of Wo so that Wo = ZZ ⊤ , and form
the SVD UΣ 2 U ⊤ of Z ⊤ WcZ. Then T is given by T = Σ 1
2 U ⊤ Z −1 .
. . . . . .
Boumediene Hamzi (Imperial College) On Control and RDS in RKHS June 4th, 2012 13 / 55