From 6dcb3d815ac60484029586b29a292a4c18837d40 Mon Sep 17 00:00:00 2001
From: caju <tiago.oliva.costa@gmail.com>
Date: Sun, 21 Mar 2021 17:25:55 -0300
Subject: [PATCH] Implement `luenberger` (#457)

Implements a wrapper around `place` which allows for a more convenient user workflow when performing pole-placement for observer design.
---
 src/synthesis.jl | 20 +++++++++++++++++++-
 1 file changed, 19 insertions(+), 1 deletion(-)

diff --git a/src/synthesis.jl b/src/synthesis.jl
index ca2dbc8ed..ae0cbecbe 100644
--- a/src/synthesis.jl
+++ b/src/synthesis.jl
@@ -125,7 +125,9 @@ dkalman(A, C, R1,R2) = Matrix(dlqr(A',C',R1,R2)')
 Calculate gain matrix `K` such that
 the poles of `(A-BK)` in are in `p`.
 
-Uses Ackermann's formula."""
+Uses Ackermann's formula.
+For observer pole placement, see `luenberger`.
+"""
 function place(A, B, p)
     n = length(p)
     n != size(A,1) && error("Must define as many poles as states")
@@ -141,6 +143,22 @@ function place(sys::StateSpace, p)
     return place(sys.A, sys.B, p)
 end
 
+"""
+    luenberger(A, C, p)
+    luenberger(sys::StateSpace, p)
+
+Calculate gain matrix `L` such that the poles of `(A - LC)` are in `p`.
+Uses sytem's dual form (Controllability-Observability duality) applied to Ackermann's formula.
+That is, `(A - BK)` is indentic to `(A' - C'L') == (A - LC)`.
+"""
+function luenberger(A, C, p)
+    place(A', C', p)'
+end
+
+function luenberger(sys::StateSpace, p)
+    return luenberger(sys.A, sys.C, p)
+end
+
 #Implements Ackermann's formula for placing poles of (A-BK) in p
 function acker(A,B,P)
     n = length(P)