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Balanced Truncation and Matlab

qSuppose *s**r *» *s**r+1* for some* r* then the balanced
realization implies that those states corresponding to the singular
values of *s**r+1**,…,**s**n* are less controllable and
observable than those states corresponding to *s**1**,…,**s**r*. Therefore, truncating those less controllable and observable
states will not lose much information about the system.

qMATLAB: