Merge pull request #939 from JuliaControl/resolvent

add functions returning the resolvent of a system

Author: baggepinnen

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,

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

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