N(8) u(8) y(s) J(8) Q(8) Figure 6.3: The DGKF parameterization of all stabilizing compensators satisfying F(N(s),K(s)川ls< Definition 6.1 (Riccati Solution)Ass ume that the algebraic Riccati equation A X+XA-XRX +Q=0 has a unique s tabil izing solution X, i.e. a solution for which the eigenvalues of a-rx are all negative. This solution will be denoted by X= Ric(H) where h is the associated Hamiltonian matri T R (6.14) Theorem 6.1(The Ho Subopt imal Control Problem) This formulation cf the solu tion has been taken from/Dai90/. Let N(s be given by its state space realization A, B, C, D and introduce the notation A B1 B N(s)= C1 Du D12 15) where b, C, and d are partitioned consistenty with d, e, u, and y. Now, make the following assumptions 1.(A, B1) and(A, B2)are stabilizable(controllable 2.(C1, A)and(C2, A)are detectable (observable) D12=I and D21 Da1=1. D D21 (6.16) and soloe the two Riccati equation A-B2DICU B,Bt-B2BA CTDED D2C1)2 (6.17)￾
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