From 0a2f41295a80c1f62843593ec607b8c186be872d Mon Sep 17 00:00:00 2001
From: Fredrik Bagge Carlson <baggepinnen@gmail.com>
Date: Wed, 23 Oct 2024 10:43:19 +0200
Subject: [PATCH] add functions returning the resolvent of a system

---
 .../src/ControlSystemsBase.jl                 |  2 ++
 .../src/sensitivity_functions.jl              | 29 +++++++++++++++++++
 .../test/test_connections.jl                  | 12 ++++++++
 3 files changed, 43 insertions(+)

diff --git a/lib/ControlSystemsBase/src/ControlSystemsBase.jl b/lib/ControlSystemsBase/src/ControlSystemsBase.jl
index bc9fd9793..62177631c 100644
--- a/lib/ControlSystemsBase/src/ControlSystemsBase.jl
+++ b/lib/ControlSystemsBase/src/ControlSystemsBase.jl
@@ -80,6 +80,8 @@ export  LTISystem,
         output_comp_sensitivity,
         G_PS,
         G_CS,
+        resolvent,
+        input_resolvent,
         # Discrete
         c2d,
         c2d_x0map,
diff --git a/lib/ControlSystemsBase/src/sensitivity_functions.jl b/lib/ControlSystemsBase/src/sensitivity_functions.jl
index fe64b966c..e84d7b0c5 100644
--- a/lib/ControlSystemsBase/src/sensitivity_functions.jl
+++ b/lib/ControlSystemsBase/src/sensitivity_functions.jl
@@ -173,3 +173,32 @@ function extended_gangoffour(P, C, pos=true)
     end
 end
 
+"""
+    input_resolvent(sys::AbstractStateSpace)
+
+Return the input-mapped resolvent of `sys`
+```math
+(sI - A)^{-1}B
+```
+i.e., the system `ss(A, B, I, 0)`.
+"""
+function input_resolvent(sys::AbstractStateSpace)
+    A,B,C,D = ssdata(sys)
+    ss(A, B, I, 0, timeevol(sys))
+end
+
+"""
+    resolvent(sys::AbstractStateSpace)
+
+Return the resolvent of `sys`
+```math
+(sI - A)^{-1}
+```
+i.e., the system `ss(A, I, I, 0)`.
+
+See also [`input_resolvent`](@ref).
+"""
+function resolvent(sys::AbstractStateSpace)
+    A,B,C,D = ssdata(sys)
+    ss(A, I(sys.nx), I, 0, timeevol(sys))
+end
\ No newline at end of file
diff --git a/lib/ControlSystemsBase/test/test_connections.jl b/lib/ControlSystemsBase/test/test_connections.jl
index ce024bf10..e84b88e9f 100644
--- a/lib/ControlSystemsBase/test/test_connections.jl
+++ b/lib/ControlSystemsBase/test/test_connections.jl
@@ -416,4 +416,16 @@ function feedback_ctrl(G, K)
 end
 @test_throws ErrorException feedback_ctrl(tf([1], [0.1, 1]), delay(0.1))
 
+Pr = resolvent(P)
+@test Pr.A == P.A
+@test Pr.B == I
+@test Pr.C == I
+@test iszero(Pr.D)
+
+Pr = input_resolvent(P)
+@test Pr.A == P.A
+@test Pr.B == P.B
+@test Pr.C == I
+@test iszero(Pr.D)
+
 end
\ No newline at end of file