MIMO SYSTEM DESIGN METHOD 2 –MODIFIED SINGLE- LOOP EQUIVALENTS
The design technique of Chapter 6 inherently involves some over-design, as seen from Eq. (6.l), in which t21, t31 can be any members of their acceptable sets τ21,τ31 and q12,q13 any member of their uncertainty sets. As noted in Sec. 6-2, it is therefore necessary to use the worst case values which leads to over-design. Actually, in the real world, there is a correlation between the t21,t31 and the q11,q13, etc. For example, in Eq. (5.55) it is possible that q12 is large when t21 is large in the expression for c11. Such a correlation can only help make c11 smaller. Thus, for Method 1, it is not possible to use this correlation, and so one must take the largest t21, the smallest q12, etc. This is the price paid for converting the MIMO problem into the much simpler MISO problems, and avoiding having to work with the horrendous denominator in Eq. (5.25).