Summary: 1030 IEEE TRANSACTlONSONAUTOMATIC COhTROL. VOL.AC-30, NO. 10,0(3TOBER 1985
which, in general, is not zero. Without this term, the system(A.8)-(A. 10)
has an equihbriumat the originfm= 0, f = 0,e = 0, suitablefor a local
stability analysisby linearization. After this analysis, the extent of local
stabilityproperties should be tested by reintroducing the forcing term-
yw*e* as a perturbation. The linearization of (A.8)-(A.10)aroundthe
origin leaves (A.8) unchanged while (A.9)-(A.10) becomes
[-1-3= [-y(w,hr+A, e*Q j bw:]o [-;-I+ [ 0 ]f m .
Since (A.8) does not depend on f or 8 and is u.a.s., the local stability
properties of the zero solution of (A.8)-(A.10) are determined by the
properties of the system
Ife, is small,the term ye*C canbe treatedas a perturbation and stability
analysis is performed without it, that is, on the system (1.1).
DiscussionswithK. Astrom, R. Bitmead, R. Kosut, C. R. Johnson,
S.S.Sastry, P. Ioannou,and L.Praly contributed tothe formulationof the
stabilitycriterion in this note.