# control.matlab.care¶

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

(X, L, G) = care(A, B, Q, R=None) solves the continuous-time algebraic Riccati equation where A and Q are square matrices of the same dimension. Further, Q and R are a 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 and the closed loop eigenvalues L, i.e., the eigenvalues of A - B G.

(X, L, G) = care(A, B, Q, R, S, E) solves the generalized continuous-time algebraic Riccati equation 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 = R^-1 (B^T X E + 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()`.