Section 6.1 The Quasi-Ho Smith Predictor Case 1: Consider the following stable rational plant of MP: KN_(s) G(5)=M-(5) where K is the gain,N-(s)and M-(s)are the polynomials with roots in the LHP,N_(0)=M-(0)=1,and deg{N-}<deg{M-}. It is easy to control such a plant.For the Hoo performance index and the weighting function W(s)=1/s we have llW(s)s(s)ll lW(s)[1-G(s)Q(s)]lloo ≥0 The following controller is the optimal one: Qopt(s)= M_(s) KN_(s) 4口，+@，4定4=定0C Zhang.W.D..CRC Press.2011 Version 1.0 5/74Section 6.1 The Quasi-H∞ Smith Predictor Case 1: Consider the following stable rational plant of MP: G(s) = KN−(s) M−(s) where K is the gain, N−(s) and M−(s) are the polynomials with roots in the LHP, N−(0) = M−(0) = 1, and deg{N−} ≤ deg{M−}. It is easy to control such a plant. For the H∞ performance index and the weighting function W (s) = 1/s we have kW (s)S(s)k∞ = kW (s)[1 − G(s)Q(s)]k∞ ≥ 0 The following controller is the optimal one: Qopt(s) = M−(s) KN−(s) Zhang, W.D., CRC Press, 2011 Version 1.0 5/74