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.

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. ${\displaystyle f}$ is Hurwitz stable) is that

where ${\displaystyle \Delta _{i}}$ is the i-th principal minor of the Hurwitz matrix associated with ${\displaystyle f}$.

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