dhfnorm (Mu Analysis and Synthesis Toolbox)

Mu Analysis and Synthesis Toolbox

dhfnorm

dhfnorm computes the H gain of a stable, discrete-time SYSTEM matrix

Syntax

```
out = dhfnorm(sys,ttol,h,iiloc)
```

Description
dhfnorm computes the H norm of a stable, discrete-time SYSTEM. It converts the SYSTEM to continuous-time via a bilinear transformation and then calls the routine hinfnorm.

The method uses the bilinear transformation from the z-plane to the s-plane given by,

where h is the time between samples. This is a transformation between the unit disk and the left half plane. If the system p has a pole close to z = -1, then a preliminary output feedback is used to move such poles before the bilinear transformation is performed.

Input arguments

sys
SYSTEM matrix (discrete-time), CONSTANT or VARYING matrix

ttol
relative tolerance of accuracy for SYSTEM matrices only,(default = 0.001)

h
time between samples (default 1)

iiloc
initial estimate of worst case frequency (optional)

:

`sys`	SYSTEM matrix (discrete-time), CONSTANT or VARYING matrix
`ttol`	relative tolerance of accuracy for SYSTEM matrices only,(default = 0.001)
`h`	time between samples (default 1)
`iiloc`	initial estimate of worst case frequency (optional)

Output arguments:

out
a 1 x 3 vector giving a lower bound, upper bound and the frequency where the lower bound occurs.

`out`	a 1 x 3 vector giving a lower bound, upper bound and the frequency where the lower bound occurs.

Reference
Doyle, J.C., K. Glover, P. Khargonekar, and B. Francis, "State-space solutions to standard H₂ and H control problems," IEEE Transactions on Automatic Control, vol. 34, no. 8, pp. 831-847, August 1989.

See Also
hinfsyne, hinffi, hinfnorm, hinfsyn, h2syn, h2norm, ric_eig, ric_schr, sdhfnorm, sdhfsyn

csord dhfsyn