//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