Mu Analysis and Synthesis Toolbox |

Calculate the H_{2}, H norms of a SYSTEM matrix

**Syntax**

`out`

= h2norm(sys) out = hinfnorm(sys,`tol`

)

**Description**

`h2norm`

calculates the 2-norm of a stable, strictly proper SYSTEM matrix. The output is a scalar, whose value is the 2-norm of the system.

`hinfnorm`

is a 1 x 3 vector, `out`

, which is made up (in order) of a lower bound for ||`sys`

||`sys`

||
The ||·||_{·} norm calculation is an iterative process and requires a test to stop. The variable `tol`

specifies the tolerance used to calculate the ||`sys`

||_{·}. The iteration stops when

`tol`

) x (the current lower bound).
The default value of `tol`

is 0.001.

**Algorithm**

The H_{2}` `

norm of a SYSTEM follows from the solution to the Lyapunov equation.

with ||`sys`

||_{2} = *trace* (*CXC*** '**).

`norm`

requires checking for `norm`

of the SYSTEM matrix is less than . If the matrix `norm`

can be obtained.
**Reference**

Boyd, S., K. Balakrishnan and P. Kabamba, "A bisection method for computing the H norm of a transfer matrix and related problems," *Math Control Signals and Systems,* 2(3), pp. 207-219, 1989.

**See Also**

`hinfsyn`

, `h2syn`

, `ric_eig`

, `ric_schr`

getiv, sortiv, tackon | h2syn |