init

FOTF Toolbox/@fotf/isstable.m

@@ -0,0 +1,34 @@
+function [K,alpha0,apol,p]=isstable(G,a0)
+% isstable - check whether an FOTF object is stable or not
+%
+%   [K,alpha,apol]=isstable(G)
+% 
+%   G - an FOTF object
+%   K- identifier to indicate the stability of G, returns 0, and 1
+%   alpha - the common order
+%   apol - all the pseudo poles of the system
+
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 28 March, 2017 
+% Last modified 18 May, 2022 
+   [n0,m0]=size(G); K=1; if nargin==1, a0=0.001; end
+   for i=1:n0, for j=1:m0
+      g=G(i,j); a=g.den.na; a1=fix(a/a0);
+      if length(a1)==1 && a1==0
+      else
+         [g1,alpha]=fotf2cotf(g); c=g1.den{1};
+         alpha0(i,j)=alpha; p0=roots(c); kk=[];
+         for k=1:length(p0)
+            a=g.den.a; na=g.den.na; pa=p0(k)^(1/alpha);
+            if norm(a*[pa.^na'])<1e-6, kk=[kk,k]; end
+         end
+         p=p0(kk); subplot(n0,m0,(i-1)*m0+j),
+         plot(real(p),imag(p),'x',0,0), xm=xlim;
+         if alpha<1, xm(1)=0; else, xm(2)=0; end
+         apol=min(abs(angle(p))); K=K*(apol>alpha*pi/2);
+         a1=tan(alpha*pi/2)*xm; a2=tan(alpha*pi)*xm; 
+         line(xm,a1), line(xm,-a1), line(xm,a2), line(xm,-a2)
+         xlabel('Real Axis'), ylabel('Imaginary Axis')
+   end, end, end
+   title('Pole Map')
+end