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, Observer-based Controllers for (Max-Plus)-Linear Systems

L. Hardouin, Y. Shang, C. A. Maia, and B. Cottenceau, , 2010.

L. //-matrice-d'tat-smatrix,

, DRAFT smatrix CA, 2016.

G. Smatrix,

P. Smatrix,

, A(2,2)=gd(1,4)

, //(g?1,d?4)

, A(2,1)=gd(0,6)

, A(2,0)=gd(0,1)

, A(0,2)=gd(2,0)

, // matrix of inputs

, smatrix As=star(A

, CA=otimes

/. Ab=otimes,

, CAB=otimes

/. ,

. Ar=otimes,

, CAR=otimes

/. Ca-*-r, the disturbance output transfer matrix cout<<" CAR"<<CAR<<endl

(. L1=rfrac and . Ab, CAB

. L2=rfrac,

(. Lopt=inf and . L1, , vol.2

, Lopt noncausal

. Loptcausal=prcaus,

, // the causal projection of the oberver matrix Lopt=Loptcausal

, Lopt causal

, // Below we check the Corollary 2 smatrix Yu

. Yu=otimes,

(. Yu=oplus and Y. ,

(. Yu=star and . Yu,

, Yu=otimes

. Yu=otimes,

Y. Smatrix,

. Yw=otimes,

(. Yw=oplus and Y. ,

. Yw=star, Yw

, DRAFT Yw=otimes, 2016.

(. Yw=otimes and . Yw, Loptcausal

(. Yw=otimes and . Yw, CAR

). Yu==yw and . Cout&lt;&lt;, Corollary 2 is satified, the estimated output and the real output are equal cout<<

. Yw,

}. Gref=cab,

, // reference model is chosen equal to the system, we want to keep the inp cout<<, Gref "<<Gref<<endl

(. Popt=lfrac and . Gref, CAB

. //-the-prefilter and . Cout&lt;&lt;, Popt non causal "<<Popt<<endl

P. Smatrix,

, Popt causal "<<Popt_causal<<endl

(. Kopt=otimes and . Ab, Popt

. Kopt=rfrac,

(. Kopt=lfrac and . Kopt, Popt

, Kopt non causal"<<Kopt<<endl

, // the state feedback controller

. Fopt=rfrac,

, // causal projection Kopt=prcaus(Kopt

. Fopt=prcaus,

, Fopt "<<Fopt<<endl

, Kopt "<<Kopt<<endl

, From now I try to enlighten that the strategy with oberverbasedcontrol is better // the feedback, I need your help Ying

. Foptc=otimes,

X. Xu,

. Xu=otimes,

(. Xu=oplus and . Xu,

(. Xu=star and . Xu,

. Xu=otimes,

(. Xu=otimes and . Kopt, Xu

/. Kopt,

. Xw=otimes,

(. Xw=oplus and X. ,

. Xw=star, Xw

(. Xw=otimes and . Xw, Lopt

. Xw=otimes,

(. Xw=otimes and . Kopt, Xw

/. Kopt, A+LoptC) * )(LoptCA * )R