Function File: [l, p, e] = lqe (sys, q, r)

Function File: [l, p, e] = lqe (sys, q, r, s)

Function File: [l, p, e] = lqe (a, g, c, q, r)

Function File: [l, p, e] = lqe (a, g, c, q, r, s)

Function File: [l, p, e] = lqe (a, [], c, q, r)

Function File: [l, p, e] = lqe (a, [], c, q, r, s)

Kalman filter for continuous-time systems.

.
x = Ax + Bu + Gw   (State equation)
y = Cx + Du + v    (Measurement Equation)
E(w) = 0, E(v) = 0, cov(w) = Q, cov(v) = R, cov(w,v) = S

Inputs

sys

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

a

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

g

Process noise matrix of continuous-time system (n-by-g). If g is empty [], an identity matrix is assumed.

c

Measurement matrix of continuous-time system (p-by-n).

q

Process noise covariance matrix (g-by-g).

r

Measurement noise covariance matrix (p-by-p).

s

Optional cross term covariance matrix (g-by-p), s = cov(w,v). If s is empty [] or not specified, a zero matrix is assumed.

Outputs

l

Kalman filter gain matrix (n-by-p).

p

Unique stabilizing solution of the continuous-time Riccati equation (n-by-n). Symmetric matrix. If sys is a discrete-time model, the solution of the corresponding discrete-time Riccati equation is returned.

e

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

Equations

.
x = Ax + Bu + L(y - Cx -Du)          

E = eig(A - L*C)

See also: dare, care, dlqr, lqr, dlqe.

Package: control