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Jury's array in symbolic way

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29 Nov 2011 (Updated )

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

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Description

[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; (b) 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);

Developed by Carlos M. Vélez S., cmvelez@eafit.edu.co
http://sistemascontrol.wordpress.com/
EAFIT University, http://www.eafit.edu.co
Medellín, Antioquia, Colombia
November 29th 2011

Required Products Symbolic Math Toolbox
MATLAB
MATLAB release MATLAB 7.10 (R2010a)
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Updates
30 Nov 2011

It is introduced the input argument N: digits to be considered zero a number. E.g, for N=5, 10^(-5) is considered a zero. By default, N=10

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