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//isstable True for stable filter
// FLAG = ISSTABLE(B,A) returns a logical output, FLAG, equal to TRUE if
// the filter specified by numerator coefficients B, and denominator
// coefficients A, is stable. Input vectors B, and A define a filter with
// transfer function:
//
// jw -jw -jmw
// jw B(e) b(1) + b(2)e + .... + b(m+1)e
// H(e) = ---- = ------------------------------------
// jw -jw -jnw
// A(e) a(1) + a(2)e + .... + a(n+1)e
//
// FLAG = ISSTABLE(SOS) returns TRUE if the filter specified using the
// second order sections matrix, SOS, is stable. SOS is a Kx6 matrix,
// where the number of sections, K, must be greater than or equal to 2.
// Each row of SOS corresponds to the coefficients of a second order
// filter. From the transfer function displayed above, the ith row of the
// SOS matrix corresponds to [bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)].
// Calling Syntax
// flag=isstable(b,a);
// flag=isstable(sos);
//Author: Parthasarathi Panda
//parthasarathipanda314@gmail.com
function isstab=isstable(varargin)
[nargout,nargin]=argn();
if (nargin==2) then//(a,b) is the input
a=varargin(1);
b=varargin(2);
//verifying type and length of input
if type(a)~=1 | type(b)~=1 then
error('check input type');
end
v=size(a);
if length(v)>2 then
error('check input dimension');
end
v=size(b);
if length(v)>2 then
error('check input dimension');
end
[n,k]=size(a);
if k==1 then
a=a';
elseif n~=1 then
error('check input dimension');
end
[n,k]=size(b);
if k==1 then
b=b';
k=n;
elseif n~=1 then
error('check input dimension');
end
elseif (nargin==1) then//sos form is given as input
sos=varargin(1);
v=size(sos);
if(v(1)>1) then
//verifying type and length of input
if type(sos)~=1 then
error('check input type');
end
if length(v)>2 then
error('check input dimension');
end
if v(2)~=6 then
error('When first input is a matrix, it must have exactly 6 columns to be a valid SOS matrix.');
end
a=1;b=1;
//converting it to rational form
for i=[1:v(1)]
a=convol(a,sos(i,1:3));
b=convol(b,sos(i,4:6));
end
else
b=1;
end
else
error('no. of inputs not matching');
end
if length(b)==1 then
isstab=1;
else
poly_a=inv_coeff(a);//constructing numerator polynomial
poly_b=inv_coeff(b);//constructing denominator polynomial
gc=gcd([poly_a,poly_b]);//computing gcd to remove common roots
[r,den]=pdiv(poly_b,gc);//dividing off gcd
time_constant=min(abs(roots(den)));//finding the minumum magnitude pole
if time_constant<=1 then//pole magnitude should be greater than 1
disp('unstable system');
isstab=0;
else
isstab=1;
end
end
endfunction
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