Function File: [x, l, g] = dare (a, b, q, r)

Function File: [x, l, g] = dare (a, b, q, r, s)

Function File: [x, l, g] = dare (a, b, q, r, [], e)

Function File: [x, l, g] = dare (a, b, q, r, s, e)

Solve discrete-time algebraic Riccati equation (ARE).

Inputs

a

Real matrix (n-by-n).

b

Real matrix (n-by-m).

q

Real matrix (n-by-n).

r

Real matrix (m-by-m).

s

Optional real matrix (n-by-m). If s is not specified, a zero matrix is assumed.

e

Optional descriptor matrix (n-by-n). If e is not specified, an identity matrix is assumed.

Outputs

x

Unique stabilizing solution of the discrete-time Riccati equation (n-by-n).

l

Closed-loop poles (n-by-1).

g

Corresponding gain matrix (m-by-n).

Equations

                          -1
A'XA - X - A'XB (B'XB + R)   B'XA + Q = 0

                                -1
A'XA - X - (A'XB + S) (B'XB + R)   (B'XA + S') + Q = 0

              -1
G = (B'XB + R)   B'XA

              -1
G = (B'XB + R)   (B'XA + S')

L = eig (A - B*G)

                             -1
A'XA - E'XE - A'XB (B'XB + R)   B'XA + Q = 0

                                   -1
A'XA - E'XE - (A'XB + S) (B'XB + R)   (B'XA + S') + Q = 0

              -1
G = (B'XB + R)   B'XA

              -1
G = (B'XB + R)   (B'XA + S')

L = eig (A - B*G, E)

Algorithm
Uses SLICOT SB02OD and SG02AD by courtesy of NICONET e.V.

See also: care, lqr, dlqr, kalman.

Package: control