## Documentation Center |

For MIMO systems the transfer functions are matrices, and relevant
measures of gain are determined by singular values, H_{∞},
and H_{2} norms, which are defined as follows:

Another important concept is the notion of singular values.

Some useful properties of singular values are:

These properties are especially important because they establish
that the greatest and least singular values of a matrix *A* are
the maximal and minimal "gains" of the matrix as the input vector *x* varies
over all possible directions.

For stable continuous-time LTI systems *G*(*s*),
the *H*_{2}-norm and the *H*_{∞}-norms are defined terms of
the frequency-dependent singular values of *G*(*jω*):

*H*_{2}-norm:

*H*_{∞}-norm:

where sup denotes the least upper bound.

Was this topic helpful?