$$ \dot{x} = A\,x + B\,u + G\,w $$$$ y = C\,x + D\,u + v $$$$ E(w) = 0,\,\, E(v) = 0,\,\, cov(w) = Q,\,\, cov(v) = R,\,\, cov(w,v) = S $$

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 $$ \dot{x} = A\,x + B\,u + L\,(y - C\, - D\,u) $$$$ E = \sigma (A - L\, C) $$

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

Source Code: lqe