The KharitonovConsistency procedure

This procedure may be used when dealing with the problem of determining if the roots of a parametric polynomial all lie within a given range.

For a parametric polynomial there is usually four Kharitonov polynomials i.e. polynomials have that have constant coefficients. It can be shown that if all the Kharitonov polynomials have the real parts of their roots of the same sign, then all the polynomials in the set will have the real part of their of the same sign. The following procedure allows to use the Kharitonov polynomials to test if there they may be roots of a parametric polynomial within a given range. Its syntax is:

 
KharitonovConsistency(Func,Vars,Gradient,procname)

with the following parameters:

• Func: a polynomial. If Func is a matrix, then the polynomial is supposed to be the characteristic polynomial of the matrix
• Vars: list of unknowns. The first one must be the unknown of the polynomial. If Func is a matrix the first name must be AXX
• Gradient: a flag that indicates if the derivatives of the polynomial with respect to the unknowns may be used (1) or not (0)
• procname: the name of the simplification procedure. The name of the created file will be procname.C

This procedure will calculate for the polynomial $P(x)$ the coefficients of the polynomial $P(x-a)$. Then the simplification procedure will consider that its input box has as first element a range for $x$ and update $a$ so that the Kharitonov polynomial will indicate if the polynomial may have a root larger than the lower bound of the first element of the box or lower than the upper bound of this interval. This procedure is intended to be used in conjunction with the procedure dealing with parametric polynomials.