Inputs

sys

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

q

State weighting matrix (n+p-by-n+p).

r

Input weighting matrix (m-by-m).

s

Optional cross term matrix (n+p-by-m). If s is not specified, a zero matrix is assumed.

Outputs

g

State feedback matrix (m-by-n).

x

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

l

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

Equations $$ \dot{x} = A\,x + B\,u,\quad x(0) = x_0 $$$$ J(x_0) = \int_0^\infty z^T Q\, z + u^T R\, u + 2\, z^T S\, u \,\, dt $$$$ z = \left[\matrix{ x \cr x_i }\right],\qquad x_i = \int_0^t r - y \,\, dt $$$$ L = \sigma (A - B\, G) $$

See also: care, dare, dlqr

Source Code: lqi