Jury's array in symbolic way

版本 1.2.1 (2.4 KB) 作者: Carlos M. Velez S.
The function gives the Jury's array from a numerical or SYMBOLIC polynomial (includes special cases)
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更新时间 2022/5/12

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[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);

引用格式

Carlos M. Velez S. (2024). Jury's array in symbolic way (https://www.mathworks.com/matlabcentral/fileexchange/34009-jury-s-array-in-symbolic-way), MATLAB Central File Exchange. 检索时间: .

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版本 已发布 发行说明
1.2.1

Minor fixes
1.2

Minimal fixes
1.1.0.0

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
1.0.0.0