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.StateSpace

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