init

FOTF Toolbox/@fotf/norm.m

@@ -0,0 +1,26 @@
+function n=norm(G,eps0)
+% norm -= norms of an FOTF object
+%
+%   norm(G), norm(G,inf)
+% 
+%   G - an FOTF object
+%   The 2-norm and infinity-norm of G can be evaluated, respectively
+
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 28 March, 2017 
+% Last modified 18 May, 2022 
+   [n,m]=size(G); if nargin==1, eps0=1e-6; end
+   for i=1:n, for j=1:m, A(i,j)=snorm(G(i,j),eps0); end, end
+   n=norm(A);
+end
+% norm of a SISO FOTF object
+function n=snorm(G,eps0)
+   j=sqrt(-1);  
+   if nargin==2 && ~isfinite(eps0) % H infinity norm, find the maximum value
+      f=@(w)-abs(freqresp(j*w,G));
+      w=fminsearch(f,0); n=abs(freqresp(j*w,G));
+   else % H2 norm, numerical integration
+      f=@(s)freqresp(s,G).*freqresp(-s,G); 
+      n=integral(f,-inf,inf)/(2*pi*j);
+   end   
+end