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//Checks for stability of Discrete time System function
//Description : A Discrete time system is stable if all poles of system function are inside unit circle
// Calling Syntax
// flag=isstable(b,a);
// flag=isstable(sos);
//It takes input b and a which are array vector of numerator and denumerator coefficients respectively also it takes second order section (sos) system function input.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
//It returns a logical flag = 1(true) if given system is stable and 0(false) otherwise
// Eample : 1
// flag = isstable([1 2],[1 -0.7 0.1])
// Output:
// flag =
//
// 1.
// Conclusion : as flag output is 1 system is stable
// Example : 2
// flag = isstable([1 2 0],[1 5 6])
//Output :
//unstable system
// flag =
//
// 0.
// Conclusion : this system is unstable as flag output is 0
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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