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The year 1992 marks the centennial anniversary of publication of
the celebrated monograph "The General Problem of Stability of
Motion" written by A. M. Liapunov. This anniversary inspires to
think about the way theory and applications have developed during
this century. The first observation one can make is that the
so-called "second method," nowadays known as the "Liapunov function
method," has received more attention than the "first method"; let
us also mention the study of critical cases, which brought more
attention recently in connection with the study of bifurcations and
with nonlinear stabilization. One of the reasons of popularity of
the Liapunov function approach might be the fact that, in many
situations in science and engineering, and not only in mechanics,
which was the main source of inspiration for the work of Liapunov,
natural Liapunov functions may be proposed, intimately connected
with the properties of the processes. It is one of the purposes of
this book to advocate this idea. From the mathematical viewpoint,
the century after the first appear ance of Liapunov's monograph has
been characterized both by general izations and by refinements of
Liapunov's ideas. But we feel that the most spectacular progress is
the understanding of the wide possibilities open for applications
by the use of Stability Theory as constructed by Liapunov a century
ago. We have tried to show some of the ideas in this direction by
start ing with our personal experience in the study of some
models."
In t.lw fHll of !!)!)2, Professor Dr. M. Alt.ar, chairman of tIw
newly established dppartnwnt or Managenwnt. wit.h Comput.er Science
at thp Homanian -American Univprsity in Bucharest (a private
univprsil.y), inl.roducod in t.he curriculum a course on
DiffenHltial Equations and Optimal Cont.rol, asking lIS to teach
such course. It was an inter8sting challengo, since for t.Iw first
tim8 wo had to t8ach such mathemaLical course for st.udents with
economic background and interosts. It was a natural idea to sl.m't
by looking at pconomic models which were described by differpntial
equations and for which problems in (\pcision making dir! ariso.
Since many or such models were r!escribed in discret.e timp, wp
eleculed to elpvolop in parallel t.he theory of differential
equations anel thaI, of discrete-timo systpms aur! also control
theory in continuous and discrete time. Tlw jll'eSPlu book is t.he
result of our tpaehing px!wripnce wit.h this courge. It is an
enlargud version of t.he actllal lectuf(~s where, depending on t.he
background of tho St.lI(\('Ilts, not all proofs could be given in
detail. We would like to express our grat.itude to tlw Board of the
Romanian - American University, personally 1. 0 the Rector,
Professor Dr. Ion Smedpscu, for support, encouragement and
readinpss to accept advancnd ideas in tho curriculum. fhe authors
express t.heir warmest thanks 1.0 Mrs. Monica Stan . Necula for tho
oxcellent procC'ssing of t.he manuscript.
In t.lw fHll of !!)!)2, Professor Dr. M. Alt.ar, chairman of tIw
newly established dppartnwnt or Managenwnt. wit.h Comput.er Science
at thp Homanian -American Univprsity in Bucharest (a private
univprsil.y), inl.roducod in t.he curriculum a course on
DiffenHltial Equations and Optimal Cont.rol, asking lIS to teach
such course. It was an inter8sting challengo, since for t.Iw first
tim8 wo had to t8ach such mathemaLical course for st.udents with
economic background and interosts. It was a natural idea to sl.m't
by looking at pconomic models which were described by differpntial
equations and for which problems in (\pcision making dir! ariso.
Since many or such models were r!escribed in discret.e timp, wp
eleculed to elpvolop in parallel t.he theory of differential
equations anel thaI, of discrete-timo systpms aur! also control
theory in continuous and discrete time. Tlw jll'eSPlu book is t.he
result of our tpaehing px!wripnce wit.h this courge. It is an
enlargud version of t.he actllal lectuf(~s where, depending on t.he
background of tho St.lI(\('Ilts, not all proofs could be given in
detail. We would like to express our grat.itude to tlw Board of the
Romanian - American University, personally 1. 0 the Rector,
Professor Dr. Ion Smedpscu, for support, encouragement and
readinpss to accept advancnd ideas in tho curriculum. fhe authors
express t.heir warmest thanks 1.0 Mrs. Monica Stan . Necula for tho
oxcellent procC'ssing of t.he manuscript.
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