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. |
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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 |