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 $$ \dot{x} = A\,x + B\,u,\quad x(0) = x_0 $$$$ J(x_0) = \int_0^\infty x^T Q\, x + u^T R\, u + 2\, x^T S\, u \,\, dt $$$$ L = \sigma (A - B\, G) $$

See also: care, dare, dlqr, lqry, lqi, lqg

Source Code: lqr