Categories &

Functions List

Function Reference: care

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

Solve continuous-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 continuous-time Riccati equation (n-by-n).
l
Closed-loop poles (n-by-1).
g
Corresponding gain matrix (m-by-n).

Equations

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

      -1
 G = R  B'X

      -1
 G = R  (B'X + S')

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

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

      -1
 G = R  B'XE

      -1
 G = R  (B'XE + S)

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

Algorithm
Uses SLICOT SB02OD and SG02AD, Copyright (c) 1996-2025, SLICOT, available under the BSD 3-Clause (License and Disclaimer).

See also: dare, lqr, dlqr, kalman

Source Code: care