q S1=diag(s1Is1, s2Is2,…, srIsr),
q S1=diag(sr+1 Isr+1, sr+2Isr+1,…, sNIsN)
q Then the truncated system
q
q
q is stable and satisfies an additive error bound:
q ||G(s)-Gr(s)||¥ £2(sr+1+sr+2+…+sN)
q Frequency weighted balanced truncation method is also presented.