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 (i.e.
where
Using the same notation as above, the Liénard–Chipart criterion is that
-
a n > 0 , a n − 2 > 0 , … ; Δ 1 > 0 , Δ 3 > 0 , … -
a n > 0 , a n − 2 > 0 , … ; Δ 2 > 0 , Δ 4 > 0 , … -
a n > 0 , a n − 1 > 0 , a n − 3 > 0 , … ; Δ 1 > 0 , Δ 3 > 0 , … -
a n > 0 , a n − 1 > 0 , a n − 3 > 0 , … ; Δ 2 > 0 , Δ 4 > 0 , …
Hence one can see that by choosing one of these conditions, the number of determinants required to be evaluated is reduced.