qSuppose sr »sr+1for some r then the balanced
realization implies that those states corresponding to the singular
values of sr+1,…,snare less controllable and
observable than those states corresponding to s1,…,sr. Therefore, truncating those less controllable and observable
states will not lose much information about the system.
•>>[Ab,Bb,Cb,sig,Tinv]=balreal(A,B,C); %sig is a vector of
Hankel singular values and Tinv=T-1;
•>> [Gb,sig] = sysbal(G);
•>> Gr= strunc(Gb,2); %truncate to the second-order.