lqry

Form linear-quadratic (LQ) state-feedback regulator with output weighting

Syntax

[K,S,e] = lqry(sys,Q,R,N)

Description

Given the plant

$\begin{array}{l} \dot{x} = A x + B u \\ y = C x + D u \end{array}$

or its discrete-time counterpart, lqry designs a state-feedback control

$u = - K x$

that minimizes the quadratic cost function with output weighting

$J (u) = \int_{0}^{\infty} (y^{T} Q y + u^{T} R u + 2 y^{T} N u) d t$

(or its discrete-time counterpart). The function lqry is equivalent to lqr or dlqr with weighting matrices:

$[\begin{matrix} \bar{Q} & \bar{N} \\ {\bar{N}}^{T} & \bar{R} \end{matrix}] = [\begin{matrix} C^{T} & 0 \\ D^{T} & I \end{matrix}] [\begin{matrix} Q & N \\ N^{T} & R \end{matrix}] [\begin{matrix} C & D \\ 0 & I \end{matrix}]$

[K,S,e] = lqry(sys,Q,R,N) returns the optimal gain matrix K, the Riccati solution S, and the closed-loop eigenvalues e = eig(A-B*K). The state-space model sys specifies the continuous- or discrete-time plant data (A, B, C, D). The default value N=0 is assumed when N is omitted.

Examples

See LQG Design for the x-Axis for an example.

Limitations

The data $A, B, \bar{Q}, \bar{R}, \bar{N}$ must satisfy the requirements for lqr or dlqr.

Version History

Introduced before R2006a