control.care

control.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

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

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

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