Function File: [g, x, l] = lqr (sys, q, r)

Function File: [g, x, l] = lqr (sys, q, r, s)

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

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

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

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

Linear-quadratic regulator.

Inputs

sys

Continuous or discrete-time LTI model (p-by-m, n states).

a

State matrix of continuous-time system (n-by-n).

b

Input matrix of continuous-time system (n-by-m).

q

State weighting matrix (n-by-n).

r

Input weighting matrix (m-by-m).

s

Optional cross term 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

g

State feedback matrix (m-by-n).

x

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

l

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

Equations

.
x = A x + B u,   x(0) = x0

        inf
J(x0) = INT (x' Q x  +  u' R u  +  2 x' S u)  dt
         0

L = eig (A - B*G)

See also: care, dare, dlqr.

Package: control