|Mu Analysis and Synthesis Toolbox|
Calculate the H2, H norms of a SYSTEM matrix
out= h2norm(sys) out = hinfnorm(sys,
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.
hinfnormis 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
tol) x (the current lower bound).
The default value of
tol is 0.001.
sys||2 = trace (CXC').
normrequires checking for j axis eigenvalues of a Hamiltonian matrix, H, which depends on a parameter . If H has no j axis eigenvalues, then the ||·||·
normof 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 ||·||·
normcan be obtained.
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.
|getiv, sortiv, tackon||h2syn|