control.matlab.dare¶

control.matlab.dare(A, B, Q, R, S=None, E=None, stabilizing=True)¶

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

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

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. 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 eigenvalues of A - B G , E.

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

Returns

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

Notes

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