lyapunov.py 文件源码

def hsvd(sys):
    """Compute Hankel singular values of a linear system.

    Parameters
    ----------
    sys : :data:`linear_system_like`
       Linear system representation.

    Returns
    -------
    ``(len(sys),) np.array``
       Hankel singular values.

    See Also
    --------
    :class:`.Hankel`
    :func:`.balanced_transformation`

    References
    ----------
    .. [#] Glover, Keith, and Jonathan R. Partington. "Bounds on the
       achievable accuracy in model reduction." Modelling, robustness and
       sensitivity reduction in control systems. Springer Berlin
       Heidelberg, 1987. 95-118.

    .. [#] https://www.mathworks.com/help/control/ref/hsvd.html
    """

    sys = LinearSystem(sys)
    R, O = control_gram(sys), observe_gram(sys)
    # sort needed to be consistent across different versions
    return np.sort(np.sqrt(abs(eig(np.dot(O, R))[0])))[::-1]