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control.dare — Python Control Systems Library 0.10.2 documentation

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

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

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 and the closed loop eigenvalues L, i.e., the (generalized) eigenvalues of A - B G (with respect to E, if specified).

Parameters:

A, B, Q2D arrays

Input matrices for the Riccati equation.

R, S, E2D arrays, optional

Input matrices for generalized Riccati equation.

methodstr, 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’.

stabilizingbool, optional

If method is ‘slycot’, unstabilized eigenvalues will be returned in the initial elements of L. Not supported for ‘scipy’.

Returns:

X2D array (or matrix)

Solution to the Riccati equation.

L1D array

Closed loop eigenvalues.

G2D array (or matrix)

Gain matrix.

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