9.2.NOMINAL PERFORMANCE 189 = 之一1 (8.1-8) Letπ：，；=l,.,ξbe the unstable roots(including z=l)of the least common denominator of p*(z),v"(z)with multiplicity mi.Recall that according to the assumption of Thm.9.2-1,v"(z)has at least as many poles at z=1 asp"()and each strictly unstable pole of u"(z)is also a pole of p"(z).The system type and the internal stability requirements can be unified as dk 1-g-(eB(a》=0,k=0,m-1:i=1,…5 (9.2-21 We can write -1 B()=∑ 0 9.2-22) where M=∑m: 9.2-23) =1 and compute the coefficients bj,j=0.....-1 from (9.2-21).Note that since none of the r:'s is 0 or c.(9.2-21)is equivalent to d 1g-ABfA) =0,k=0,..m:-1、i=1..502-24) Since both (-)and B(A-)are polynomials their derivatives with respect toA can be computed easily.Equation (9.2-24)yields a system of linear equations with M unknowns (bo,b1,...,bM-1).The resulting controller (=combines the desirable properties of the H2-optimal controller and deadbeat type controllers, as explained in Sec.8.1.2. 9.2.3 Anti-aliasing Prefilter If the designer decides to add a prefilter y(s)in the block structure (Fig.7.1-1A), it should be such that the system type (asymptotic properties)and the internal stability requirements are satisfied. Section 7.5.2 discussed in detail the design of (s)so that the systemn type is preserved.When the only unstable poles of p"()are at-1 (i.e..of p(s)at s =0),the assumption of Thm.9.2-1 that v"(z)has at least as many poles at