HANKELSV

HANKELSV computes Hankel singular values and grammians. (Improved version of HKSV)

HANKELSV computes controllability and observability grammians Wc, Wo, and the Hankel singular values OUT of an LTI model SYS (created with either TF, ZPK, SS, or FRD). The model SYS can be either continuous-time or discrete-time. However, only in continuous-time case that SYS is allowed to be unstable. The computed Hankel singular values are sorted in ascending order. For unstable continuous-time system, state-space stable/anti-stable decomposition is used instead and OUT = [OUT_stable;OUT_anti-stable]. In addition, Wc={Wc_stable,Wc_anti-stable} and Wo is either.

Note that the former version of HKSV employs an obsolete fashion in using the MATLAB function GRAM, i.e., instead of using GRAM(SYS,'c') and GRAM(SYS,'o'), it uses GRAM(A,B) and GRAM(A',C'), respectively. This restricts the computation of gramians to continuous-time case, only, since GRAM(A,B) and GRAM(A',C') solve LYAP, not DLYAP. This improved version also correct some other bugs in the former version, for example, HKSV does not return gramians when SYS is unstable, but not anti-stable.