Mu Analysis and Synthesis Toolbox | ![]() ![]() |
Calculate the H2, H norms of a SYSTEM matrix
Syntax
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.
The output from hinfnorm
is a 1 x 3 vector, out
, which is made up (in order) of a lower bound for ||sys
||·, an upper bound for ||sys
||·, and a frequency, o, at which the lower bound is achieved.
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
(the current upper bound) (1 +
tol
) x (the current lower bound).
The default value of tol
is 0.001.
Algorithm
The H2
norm of a SYSTEM follows from the solution to the Lyapunov equation.
Calculation of the H
norm
requires checking for j axis eigenvalues of a Hamiltonian matrix, H
, which depends on a parameter
. If H
has no j
axis eigenvalues, then the ||·||·
norm
of the SYSTEM matrix is less than . If the matrix H
does have j
axis eigenvalues, then these occur at the frequencies where the transfer matrix has a singular value (not necessarily the maximum) equal to
. By iterating, the value of the ||·||·
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.
Boyd, S., and K. Balakrishnan, "A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its H norm," Systems and Control Letters, vol. 15-1, 1990.
Bruinsma, O., and M. Steinbuch, "A fast algorithm to compute theH norm of a transfer function matrix," Systems and Control Letters, vol. 14, pp. 287-293, 1990.
See Also
hinfsyn
, h2syn
, ric_eig
, ric_schr
![]() | getiv, sortiv, tackon | h2syn | ![]() |