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Yes / No Higher order polynomial
Higher Yes / No
Yes / No 2008/09 MECH466 : Automatic Control 25 Why no proof in textbooks? “most undergraduate students are exposed to the
Routh–Hurwitz criterion in their first introductory
controls course. This exposure, however, is at the
purely algorithmic level in the sense that no attempt
is made whatsoever to explain why or how such an
MECH466 : Automatic Control MECH466 : Automatic Control 26 Why no proof in textbooks? (cont’d) An Elementary Derivation of the Routh–Hurwitz Criterion
Ming-Tzu Ho, Aniruddha Datta, and S. P. Bhattacharyya
IEEE Transactions on Automatic Control
vol. 43, no. 3, 1998, pp. 405-409. 2008/09 2008/09 27 “The principal reason for this is that the classical
proof of the Routh-Hurwitz criterion relies on the
Routhnotion of Cauchy indexes and Sturm’s theorem,
both of which are beyond the scope of
“Routh-Hurwitz criterion has become one of the few
Routhresults in control theory that most control engineers
are compelled to accept on faith.”
2008/09 MECH466 : Automatic Control 28 7 Summary and Exercises
Stability for LTI systems
(BIBO, asymptotically) stable, marginally stable, unstable
Stability for G(s) is determined by poles of G.
G(s) Routh-Hurwitz stability criterion to determine stability
Routhwithout explicitly computing the poles of a system
Next, examples of Routh-Hurwitz criterion
Read Sections 6.1 & 6.2.
Solve Problems 6.1, 6.9 & 6.14.
Solve No lecture on next Tuesday (Jan. 27)
2008/09 MECH466 : Automatic Control 29 8...
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- Winter '09