In control theory, the Liénard–Chipart criterion is a stability criterion modified from the Routh–Hurwitz stability criterion, proposed in 1914 by French physicists 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
f ( z ) = a 0 z n + a 1 z n − 1 + ⋯ + a n , a 0 > 0 {\displaystyle f(z)=a_{0}z^{n}+a_{1}z^{n-1}+\cdots +a_{n},\quad a_{0}>0}
to have negative real parts (i.e. f is Hurwitz stable) is that
Δ 1 > 0 , Δ 2 > 0 , … , Δ n > 0 , {\displaystyle \Delta _{1}>0,\,\Delta _{2}>0,\ \ldots ,\ \Delta _{n}>0,}
where Δi is the i-th leading principal minor of the Hurwitz matrix associated with f. Using the same notation as above, the Liénard–Chipart criterion is that f is Hurwitz stable if and only if any one of the four conditions is satisfied:
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