control.care

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

Solves the continuous-time algebraic Riccati equation.

X, L, G = care(A, B, Q, R=None) solves

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 array_like) – Input matrices for the Riccati equation

  • B (2D array_like) – Input matrices for the Riccati equation

  • Q (2D array_like) – Input matrices for the Riccati equation

  • R (2D array_like, optional) – Input matrices for generalized Riccati equation

  • S (2D array_like, optional) – Input matrices for generalized Riccati equation

  • E (2D array_like, 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