control.dare

control.dare(A, B, Q, R, S=None, E=None, stabilizing=True, method=None, _As='A', _Bs='B', _Qs='Q', _Rs='R', _Ss='S', _Es='E')[source]

Solves the discrete-time algebraic Riccati equation.

X, L, G = dare(A, B, Q, R) solves

$A^T X A - X - A^T X B (B^T X B + R)^{-1} B^T X A + Q = 0$

where A and Q are square matrices of the same dimension. Further, Q is a symmetric matrix. The function returns the solution X, the gain matrix G = (B^T X B + R)^-1 B^T X A and the closed loop eigenvalues L, i.e., the eigenvalues of A - B G.

X, L, G = dare(A, B, Q, R, S, E) solves the generalized discrete-time algebraic Riccati equation

$A^T X A - E^T X E - (A^T X B + S) (B^T X B + R)^{-1} (B^T X A + S^T) + Q = 0$

where A, Q and E are square matrices of the same dimension. Further, Q and R are symmetric matrices. If R is None, it is set to the identity matrix. The function returns the solution X, the gain matrix $G = (B^T X B + R)^{-1} (B^T X A + S^T)$ and the closed loop eigenvalues L, i.e., the (generalized) eigenvalues of A - B G (with respect to E, if specified).

Parameters

A (2D arrays) – Input matrices for the Riccati equation
B (2D arrays) – Input matrices for the Riccati equation
Q (2D arrays) – Input matrices for the Riccati equation
R (2D arrays, optional) – Input matrices for generalized Riccati equation
S (2D arrays, optional) – Input matrices for generalized Riccati equation
E (2D arrays, optional) – Input matrices for generalized Riccati 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’.
stabilizing (bool, optional) – If method is ‘slycot’, unstabilized eigenvalues will be returned in the initial elements of L. Not supported for ‘scipy’.

Returns

X (2D array (or matrix)) – Solution to the Ricatti equation
L (1D array) – Closed loop eigenvalues
G (2D array (or matrix)) – Gain matrix