lqg

Scilab Function
Last update : April 1993

lqg - LQG compensator

### Calling Sequence

  `[K]=lqg(P,r)`

### Parameters

- `P`: `syslin` list (augmented plant) in state-space form
- `r`: 1x2 row vector = (number of measurements, number of inputs) (dimension of the 2,2 part of `P`)
- `K`: `syslin` list (controller)

### Description

`lqg` computes the linear optimal LQG (H2) controller for the "augmented" plant `P=syslin('c',A,B,C,D)` (continuous time) or `P=syslin('d',A,B,C,D)` (discrete time).

The function `lqg2stan` returns `P` and `r` given the nominal plant, weighting terms and variances of noises.

`K` is given by the following ABCD matrices: `[A+B*Kc+Kf*C+Kf*D*Kc,-Kf,Kc,0]` where `Kc=lqr(P12)` is the controller gain and `Kf=lqe(P21)` is the filter gain. See example in `lqg2stan`.

### See Also

`lqg2stan`, `lqr`, `lqe`, `h_inf`, `obscont`,

### Author

F.D.