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 |