h_infinity_norm¶
Returns H-infinity norm of a linear system using iterative methods.
The H-infinity norm of a MIMO system is traditionally calculated finding the largest SVD of the transfer function evaluated across the entire frequency spectrum. That can prove costly for a large number of evaluations, hence the iterative methods of [1] are employed.
In the case of a SISO system the H-infinity norm corresponds to the maximum frequency gain.
A scalar value is returned if the system is stable. If the system is unstable it returns np.Inf
.
References
[1] Bruinsma, N. A., & Steinbuch, M. (1990). A fast algorithm to compute the H∞-norm of a transfer function matrix. Systems and Control Letters, 14(4), 287–293. https://doi.org/10.1016/0167-6911(90)90049-Z
- param ss
Multi input multi output system.
- type ss
sharpy.linear.src.libss.ss
- param **kwargs
Key-word arguments.
- keyword tol
Tolerance. Defaults to
1e-7
.- kwtype tol
float (optional)
- keyword tol_imag_eigs
Tolerance to find purely imaginary eigenvalues. Defaults to
1e-7
.- kwtype tol_imag_eigs
float (optional)
- keyword iter_max
Maximum number of iterations.
- kwtype iter_max
int (optional)
- keyword print_info
Print status and information. Defaults to
False
.- kwtype print_info
bool (optional)
- returns
H-infinity norm of the system.
- rtype
float