control.lyap

control.lyap(A, Q, C=None, E=None, method=None)[source]

Solves the continuous-time Lyapunov equation.

X = lyap(A, Q) solves

$A X + X A^T + Q = 0$

where A and Q are square matrices of the same dimension. Q must be symmetric.

X = lyap(A, Q, C) solves the Sylvester equation

$A X + X Q + C = 0$

where A and Q are square matrices.

X = lyap(A, Q, None, E) solves the generalized continuous-time Lyapunov equation

$A X E^T + E X A^T + Q = 0$

where Q is a symmetric matrix and A, Q and E are square matrices of the same dimension.

Parameters

A (2D array_like) – Input matrices for the Lyapunov or Sylvestor equation
Q (2D array_like) – Input matrices for the Lyapunov or Sylvestor equation
C (2D array_like, optional) – If present, solve the Sylvester equation
E (2D array_like, optional) – If present, solve the generalized Lyapunov equation
method (str, optional) – Set the method used for computing the result. Current methods are ‘slycot’ and ‘scipy’. If set to None (default), try ‘slycot’ first and then ‘scipy’.

Returns

X – Solution to the Lyapunov or Sylvester equation

Return type

2D array