control.lyap¶

control.lyap(A, Q, C=None, E=None)¶

X = lyap(A, Q) solves the continuous-time Lyapunov equation

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

where A and Q are square matrices of the same dimension. Further, 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) – Dynamics matrix
C (2D array, optional) – If present, solve the Slyvester equation
E (2D array, optional) – If present, solve the generalized Laypunov equation

Returns

Q – Solution to the Lyapunov or Sylvester equation

Return type

2D array (or matrix)

Notes

The return type for 2D arrays depends on the default class set for state space operations. See use_numpy_matrix().