Jury's array in symbolic way

The function gives the Jury's array from a numerical or SYMBOLIC polynomial (includes special cases)

[M, L] = jury(P,N)

This function gives the Jury's array from a numerical or SYMBOLIC polynomial and includes the two special cases:

(1) the first element of the second row of a block is zero;

(2) a row of zeros (when there are roots on unit circle or reciprocal roots like (r,1/r).

The symbolic results can be used to solve inequalities and obtain the stability intervals of symbolic vaiables.

P Numerical or symbolic array of coeficients. In the case of symbolic variables it is necesarry to define them in workspace as: >> syms a b c ...

N Digits to be considered zero a number. E.g, for N=5, 10^(-5) is considered a zero. By default, N=10

M Jury's array without any simplification (e.g., with epsilon notation)

L Simplified coefficients of first column and second row of each Jury's block (e.g., using the limit when epsilon tends to zero) that determines the place of roots: the number of roots outside the unit circle is equal to negative values in L

Examples:

1. syms z; P1 = (z-1)*(z-2)*(z-0.3)*(z^2+1); P = sym2poly(P1); [M,L] = jury(P);

2. syms z; P1 = (z-0.1)*(z-0.2)*(z-0.3)*(z^2+1); P = sym2poly(P1); [M,L] = jury(P);

3. syms a b; P = [1 a b 0.1]; [M,L] = jury(P);

4. syms a; P = [1 a 1 0.1]; [M,L] = jury(P);

5. P = [1 2 -1 -1 2 1]; [M,L] = jury(P);

6. P = [ -1.21, -0.063, 5.3, -0.063, -1.21]; [M,L] = jury(P);

7. syms z; P1 = (z+1/2)*(z+2)*(z+0.5)*(z-0.8); P = sym2poly(P1); [M,L] = jury(P);

8. P = [0.1 -0.3 0.67 0.92 0.3 -0.1]; [M,L] = jury(P);