misc.place: different to builtin place, arbitrary eigenvalues can be set, that...

misc.place: different to builtin place, arbitrary eigenvalues can be set, that includes eigenvalues of multiplicity greater than rank(B)
+ some comments.

+misc/adj.m

@@ -31,7 +31,9 @@ for n=1:size(A,1)
        adjA(m,n)=cofactor(n,m,A);           % By switching indices, the resultant matrix is transposed.
    end
 end
+end % adj()
 
 % Calculate elements of the cofactor-matrix
 function [a] = cofactor(i,j,A)
 a=(-1)^(i+j)*det(A([1:i-1, i+1:end],[1:j-1,j+1:end]));
+end % cofactor()

+misc/place.m

+function K = place(A, B, p)
+%MISC.PLACE calculates the state feedback K such that all eigenvalues of (A-B*K) will result in
+%p, i.e. eig(A-B*K) == p. Diffrent to the built-in place, this method supports eigenvalues of
+%multiplicity greater than rank(B);
+%
+% Example
+%	K = misc.place(magic(2), [0; 1], [-1, -1])
+%	eig(magic(2) - [0; 1] * K)
+
+arguments
+	A (:, :) double;
+	B (:, :) double;
+	p (:, 1) double = zeros([size(A, 1), 1]);
+end
+
+try 
+	% try matlab built-in place first, as it is more accurate
+	K = place(A, B, p);
+catch
+	assert(size(B, 2) == 1, "only tested for SISO-case yet");
+	K = zeros(size(B, 2), size(A, 1));
+	Atmp = A;
+	for it = 1 : size(A, 1)
+		[~, D, W] = eig(Atmp, "nobalance", "vector");
+		idx = chooseIdx(D, p);
+		if ~isempty(idx)
+			Ktmp = (W(:, idx)' * B) \ (D(idx) - p(it)) * W(:, idx)';
+			K = K + Ktmp;
+			Atmp = A - B*K;
+		else
+			break;
+		end
+			
+	end
+	K = real(K);
+end % try...catch
+
+end % misc.place
+
+function idx = chooseIdx(D, p)
+	% helper function
+	toBeMoved = setdiff(round(D, 15), round(p, 15));
+	if isempty(toBeMoved)
+		idx = [];
+	else
+		idx = find(round(D, 15) == toBeMoved(1), 1);
+	end
+end
\ No newline at end of file

+misc/placeLQR.m

@@ -38,7 +38,7 @@ if size(B,1)~=size(A,1)
 	error('size(B,1)~=size(A,1)!')
 end
 
-if size(B,2) ==1
+if size(B, 2) == 1
 	K = place(A,B,pD);
 	p = pD;
 else % mimo case:

+unittests/+misc/testMisc.m

@@ -4,6 +4,14 @@ function [tests] = testMisc()
 tests = functiontests(localfunctions());
 end
 
+function testPlace(tc)
+A = magic(2);
+B = ones(2, 1);
+K = misc.place(A, B, 0*B);
+tc.verifyEqual(eig(A - B*K), 0*B, "AbsTol", 1e-6);
+end % testPlace()
+
+
 function testReporter(testCase)
 
 m = misc.Message("hallo");