:py:mod:`dysys.statespacesymbolic`
==================================

.. py:module:: dysys.statespacesymbolic


Module Contents
---------------

Classes
~~~~~~~

.. autoapisummary::

   dysys.statespacesymbolic.StateSpaceSymbolic



Functions
~~~~~~~~~

.. autoapisummary::

   dysys.statespacesymbolic.sss



.. py:class:: StateSpaceSymbolic(A, B, C, D, E=None, F=None)


   Represents a continuous LTI state-space model in symbolic form

   .. py:method:: eig()

      Returns L, M: the eigenvalue and eigenvector matrices of A


   .. py:method:: diag_transformation(reals_only=False, sort=True, normalize=False)

      Return (P, D), where D is diagonal and D = P^-1 * self.A * P

      This returns self.A.diagonalize() from SymPy.

      :param reals_only: bool. Whether to throw an error if complex numbers are need
                         to diagonalize. (Default: False)
      :param sort: bool. Sort the eigenvalues along the diagonal. (Default: True)
      :param normalize: bool. If True, normalize the columns of P. (Default: False)


   .. py:method:: is_diagonalizable(reals_only=False, **kwargs)

      Returns ``True`` if self.A is diagonalizable.

      This returns self.A.is_diagonalizable() from SymPy.

      :param - reals_only: bool, optional
                           If ``True``, it tests whether the matrix can be diagonalized
                           to contain only real numbers on the diagonal.
                           If ``False``, it tests whether the matrix can be diagonalized
                           at all, even with numbers that may not be real.


   .. py:method:: state_transition_matrix(t)

      Returns the state transition matrix


   .. py:method:: state_free_response(t, x0)

      Returns the free response of the state vector


   .. py:method:: output_free_response(t, x0)

      Returns the free response of the output vector


   .. py:method:: state_forced_response(t, u)

      Returns the forced response of the state vector


   .. py:method:: output_forced_response(t, u)

      Returns the forced response of the output vector


   .. py:method:: state_response(t, x0=None, u=None)

      Returns the state response for initial condition x0 and input u


   .. py:method:: output_response(t, x0=None, u=None)

      Returns the output response for initial condition x0 and input u


   .. py:method:: to_numpy(params = {})

      Returns A, B, C, D as NumPy arrays


   .. py:method:: to_control(params = {})

      Returns an equivalent Control Systems package control.StateSpace object



.. py:function:: sss(A, B, C, D, E=None, F=None)

   Create a StateSpaceSymbolic object