SCIENTIFIC ABSTRACT ALIMOV, Y. I. - ALIMOVA, Y. K.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000101120001-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 20, 2001
• Sequence Number: 1
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

80132
S/141/59/oo2/o6/oi4/024
Overall Stability of the Equilibrium Sfj,?2/FJ8J Iy-type Control
a e 0 0 a
Systems
as W, , which satisfies the equation:
n- 8V
dVljfdt 21 - Psrxr W1 (30).
s,r=l dxS
Further, it is shown that if the elements Pij = Pji.
(such that i A- J) of the determinant D21-1 1whos e
diagonal elements satisfy Eqs 05)-07), can be chosen
in such a way that all the successive minors of' the element
are positive, the equilibrium state of the system (bserlbed
by Bqs (6) and (7) and satisfying Eqs (5) is asymptotically
stable (as regards the overall stability). The above
theorents are sultable for constructing the simplified
stability criteria of high-order systems. The systems
with n ranging from 4 to 6 are considered.
The author thanks Ye*A. Barbashin for directing this
Card3/4 work- LK-

BM32
S/l41/59/oo2/o6/ol4/024
E122~P3#2
Overall Stability of the Equilibrium Sta elay-type Control
Systems
There eire 13 Soviet references.
ASSOCIATION: Ura,llskiy politekhnicheskiy institut
(Ural Polytechnical Institute)
SUBMITTED: June 8, 1959
Card 4/4

NALMOV, Tu. 1.
Determiniag the peri!)dict\I
of noncontinuous control.
no-.9:83-&S '59-
movements Of a class of relay systems
Nauch.dokl.vye.shkoly; fize-mat.nauki
(MIA 13W
. 1.
1. Urallsidy politeldmicheskiy institut imeni S.M.Kirovao
(Slectrac relays) (Automatic control)

240)
AUTHORS: Skrotskiy, G. V., Alimov, Yu. I. SOV/56-.36-4-44/70
TITLE: The Influence of the Shape ol the Specimen on
Ferromagnetic Resonance in a Strong Radio-Frequency Field
(Vliyaniye fOrmy obreztsanaferromagnitnyy rezonans v
sillnom radiochastotnom pole)
PERIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1959,
Vol 36, Nr 4,, pp 1267-1271 (USSR)
ABSTRACT: Expuriments,13,y (Refs 1, 2) it was shown that the
decreases slowly in the direction
magnetization oomponent M
Z
of the constant field H 0 with growing microwave power. This
effect was theoretically investigated by Suhl (Refs 3, 4)
and derived by, using the Landau-Lifshits equation (1):
4
M +d -1,-# ef3
jaH . . [4M tj - 0, -1 - I/M
, cc> 0 0, for an
a
r.f. field h the amplitudes of which are great compared
1/2
to the threshold field h
: h
MAH0.08AH/41IM
)
Card 1/3 c
e
S
The authors of' the present paper analyze the exact solutions

The Influence of the Shape of -the Specimen on SOV/56--36-4-44/70
Ferromagnetic Resonance in a Strong Radio-Frequency Field
of (1) for noaspherical ferromagnetic specimens in an
r.f. field of arbitrary amplitude (they had already
derived the solutions in a previous paper (Ref 5). It is
found that above a certain value of h the motion of the
magnetization vector becomes unstable? The slow decrease
of the magnetization component and the shift of the
resonance field for field strengths h 0) h c are explained.
At hD> h c the height of the absorption peah: decreases and
its vidth increases. The results agree easentially with
those obtained by Suhl. The dependence of M z on at ~ N. 10
for different values of a is shown by figure 1; figure 2
showii the influence exercised by the nonsphericity of the
specimen upon m Z in dependence on a 2 with ~ N = 100;
the diagram, fox oomparison contains the cur,ve M Z (a2)
for a homogeneounly magnetized spherical specimen,, The
denotations apply to a system of coordinaten rotating
Card 2/3 round H 0 - Hz with the frequencyU , where (1) has the form

The Influence of the Shape of the Specimen on SOV/56-36-4-44/70
Ferromagnetic Resonance in a Strong Radio-Frequency Field
[-+ fl , [ .:~ 411 ef _-4
15 m an - 0, with via bi 0
h
-W*/U " 0
a Lj a Lj
There are 2 figures and 6 referencest I of .,hich is Soviet.
ASSOCIATIONs Urallskiy politekhnicheskiy institut (Ural Polytechnic
Institute)
SUBMITTEDs October 28, 1958
Card 3/3

ALIMOV, Yu.I.
Problom of the atavility of relay systems in automatic control.
Izv.v7,s.uch9b.zav.; mat. no.1:3-10 160. (MIRA 13:6)
1. Ural'skiy poll[tekhnicheski7 institut imeni S.M.Ki;ova.
(Automatic control)

ALIMOV, Yu.I.
New nethod of arriving at simplified criteria of absoliite stability,.
Inzh.-fiz.zhur. no.6:35-41 Je 160, (MIRA 13-7)
1. Urallskiy politekhnicheskiy, institut im. S.K.Kirova, g. Sverdlovsk.
(Automatic control)

16, si 5 o o 77 4;-~
OV/3. 03 - 2 1-1-19/2 2
AUTHM Alimo,j,
TITLE: Letter to the Editcr. Remarks on the Study by Yu. S.
Sobolev "On Absolute Stability of Some Cont-ro-1 Systems"
PERIODT'ALt Avtcn,atika I telemekhanika, 196C~ Vol 2.1, Nr 1, pp
1143 -144 (.USSR)
ABSTRACT, The study under discussion was published in Av--omatika
I telemekhanika. Vol 2-0, Nr 4, 19r,79, In this study, a
theorem establishes conditions for absolute stabilty
at certain types of control systems. The writer of
the letter shows that there are systems of 11-hi,--, type
which are stable according to Rouse-Hurwitz cor.ditions,
but which d~~ not satisfy the conditions of the above
theorem, Tt Is astated that the theorem derived by
Yu. S. Sobolev is Insufficient, to be used for solution
of probi.emo- of' Lbsolute stability. There are 2 Soviet
ref erence s .
Gard 1/-,

85648
S/103/60/021/006/020/027/XX
10,52049 (M2 ell 113,111311-V) BO19/BO63
AUTHOR: Alimoir, Yu. 1. (Sverdlovsk)
ILP
TITLE: Determination of Lyapunov Functions for Control Relay
Systems 11
PERIODICAL: Avtomatika i telemekhanika, 1960, Vol. 21, No. 6, PP. 720-728
TEXT: The author first gives the transmission function of an au*~qmaJLg___.
control system in matrix representation, and studies the --~ability of the
system in the phase space after introducing the term "trajectory of the
system". The states of equilil)rium of a class of control relay systems are
n
determined, and the relation VW - = a iix ixi+ skp9(0)G is obtained
i,j.l
for the Lyapunov function after extensive calculation, This function
holds for the systeas most frequently atudied in control theory, which
are described by the matrix equation i . Ax + bp(G'), 6' - k`x (3), where
A is a quadratic column matrix, and x, b, and k are n-dimensional column
Card 1/2

85648
Determination of Lyapunov Functions for
Control Relay Systems
3/103/60/021/006/020/027/XX
B019/BO63
matrices,. The criteria derived for the stability of these systems are ex-
pressed by the coefficients of the transmiss" fun tion. As the Lyapunov
function is represented in an invariant form Ithe above-Mentioned criteria
can be represented by elemen-~s of the matricesTA, b, and k. I. G-_ Malkin,
A~ I. Lurlye, and JU M. Letov are mentioned. ~e- A. Barbashin is thanked
for guidance and help. There are 15 Soviet references.
Card 2/2

ALIMOV, Yu. T.
Cand Phys-Math Sci -- (diss) "Several problems of the dynamics
of relay systems in automatic control." Sverd:i-ovsk, 1961.
10 pp; (Ministry of Higher and Secondary S ecialist Education
RSFSR, Ural IS)tate Univ imeni A. M. Gor'kiy~; 1',70 copies; price
not given; bibliography at end of text; (KL, 7--61 sut), 217)

22830
S/19 61/002/001/001/008
h B I I 2YB21 8
AUTHOR: Alialovi Yu,, I.
TITLE: Determination of the Lyapunov function for--systems of linear
differential equations with constant coeffiqient
PERIODICAL- SibLrskiy miatematicheskiy zhurnal, v. 2, no. 1, 1961, 3-6
TEXT: The criteria for the asymptotic stability of systems of linear dif-
ferential equations with constant coefficient are based on the existence of
a Lyapunov function whose) total derivative with reTect to time is a definite
form. These criteria are generalizations of I. G. Malkin's cr,: 'teria for
absolute stabilitr. In the present paperp thp author proves elcistence
theorems for the Iyapunov function of nonstable linear systems, The proofs
are analogous to oorresponding proofs of A. M. Lyapunov -and N. N. Krasovskiy.
The system of differential.nequations considered:
d)cs/dt _ V. I Pskxk' Psk i. const (s ........ , n) (1)
exhibits the function- n av
dir/dt - P W(x, . ..... Xn) (2)
ax sk'k
Card 1/2

DetermJnatLon of ...
22830
S/1 99J61 /'002/OC1 /001 /008
Bi I 2/B21 El
as a derivative with respect to time of the Lyapunov function: V(xj, .... 9 X~'
n
The theorems proved are: 1) If all roots of the characteristic equation of
system (1) have a negative real part, then there exists exactl3, one form V
of degree m for every positive definite form W(X,t ..... I Xn) of this degree,
which is no integral of sy,9tem (1). This form V satisfies con,! 'ition (2).
V must be positive definite. 2) If among the roots A, of the "!haracteristic
equation of system (1) there is at least one with a positive real pa and
if for non-neeative integers m which satisfy the donditiM~;
1 Mn i.1 'i = "
X M will never vanish, then there exists exactly one form 11 of degree m
for every positive definite form N of this degree, which is no integral of
system (1). This form V satisfies condition (2) and is positive definite.
3) If among the roots of the characteristic equation of system (1) there is
at least one with a positive real part, then there exists a forn V of degree
m and a positive number oc Sor every positive definite form W of this degree,
which is no integral of (1). Thus, aV/dt - aV - W, V being positive definite.
Professor Ye. A. Barbashin is thanked for guidance. There are 7 Soviet-
bloc references.
SUBMITTED: November 20, '1959
Card 2/2

gq5
S/lOY361yoj2/007/001/008
D
IL,1000 (16 31/ //:Zl/ //,3~)' D252 D302
AUTHOR-. Alimov, Yu. I. (Sverdlovsk)
TITLE: Application of Lyapunov's direct method to differen-
tial equations with non-unique right-hand sides
PERIODICA1,: iivtomatika i telemekhanika, v. 22, rxo. 7, 1961,
817-829
TEXT: A mathematical model is constructed for relay control sys-
teiiis which expresses better their physical meaning than the usual
model (differential equations with discontinuous right-hand sides).
The obtained mathematical model is considered as LA SySt(!M Of equa-
tions in contingencies to which Lyapunov's direct method can be
applied. This method which is an extension of Lyapunov's stability
theorems, consists among others of a theorem by Krasovs1.,-.yy, of the
Ye. A. Barbashin and N.N. Krasovskyy theorems, (Ref. 13: Nekotoryye
zadachi teorii ustoychivosti dvizheniya (Some Problems :in Stability
Theory), Fizmatl-riz, 1959), and D. Veksler's theorem (Re:,L-. 16: 0 teo-
remakh ustoychivosti d.lya sistem statsionarnykh differe',,_Ltsial1nykh
Card 115

Application of Lyapunov's direct... D252/D302
uravneniy, Revue des Matl,-L6matiques pures et ;q)TAicluees, vol. 3, no.1).
The normalized equations of motion of relay systeiit:; are;
f (t,31) . f I t 9x 9 T (0 t: $ x (2)
where f (t,x, and 0 there exists a set Ee C- El , mes Ee < and there exists
a positive number n(C) so that U Fn(p) - F(P)IIM(R)< holdo for all
pr-E'\E,r and n>n(S~). The function f(p) is called countable -valued on
El if F(EI) is a countable set, where the inverse images of the points of
M(R) are measurable Belts for the mapping F(p) of E into M(R). f(p) is
called measurable if there! exists a sequence of countsble-valued functions
fn(p) converging almost uniformly on SI with respect to f(p).
The integral of a measurable f(p) is defined by
( f(P)dp = (B) ~ F(p)dp
j~l El
where (B) denotes a 2ochner - integral. Let E be the number iine, The
Card 2/.

S/020/61/140,/001/00'1/024
on the theory of dynamic syutems 0111/C222
The derivative of an anbiguoua f(t) , tCE , is defined by
ALLtl - nin Sllt-!~'- f(t)
dt h-i,O h
where the limit value correnponds to the metric introduced above.
Given the differential equaUon
x - f(t,.X) M
where f(t,x) is an ambiguouz function defined for xCR, -oo.< t