Liénard–Chipart criterion
In control system theory, the Liénard–Chipart criterion is a stability criterion modified from the Routh–Hurwitz stability criterion, proposed by A. Liénard and M. H. Chipart. This criterion has a computational advantage over the Routh–Hurwitz criterion because it involves only about half the number of determinant computations.Algorithm
The Routh–Hurwitz stability criterion says that a necessary and sufficient condition for all the roots of the polynomial with real coefficients
to have negative real parts is that
where is the i-th leading principal minor of the Hurwitz matrix associated with.
Using the same notation as above, the Liénard–Chipart criterion is that is Hurwitz-stable if and only if any one of the four conditions is satisfied:
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Hence one can see that by choosing one of these conditions, the number of determinants required to be evaluated is reduced.
