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Give, and it shall be given unto you. ST. LUKE, VI, 38. The book is
based on several courses of lectures on control theory and appli
cations which were delivered by the authors for a number of years
at Moscow Electronics and Mathematics University. The book,
originally written in Rus sian, was first published by Vysshaya
Shkola (Higher School) Publishing House in Moscow in 1989. In
preparing a new edition of the book we planned to make only minor
changes in the text. However, we soon realized that we like many
scholars working in control theory had learned many new things and
had had many new insights into control theory and its applications
since the book was first published. Therefore, we rewrote the book
especially for the English edition. So, this is substantially a new
book with many new topics. The book consists of an introduction and
four parts. Part One deals with the fundamentals of modern
stability theory: general results concerning stability and
instability, sufficient conditions for the stability of linear
systems, methods for determining the stability or instability of
systems of various type, theorems on stability under random
disturbances."
At the beginning of this century Emil Picard wrote: "Les equations
differentielles de la mecanique classique sont telles qu 'il en
resulte que le mouvement est determine par la simple connaissance
des positions et des vitesses, c 'est-a-dire par l 'etat a un
instant donne et a ['instant infiniment voison. Les etats
anterieurs n'y intervenant pas, l'heredite y est un vain mot. L
'application de ces equations ou le passe ne se distingue pas de l
'avenir, ou les mouvements sont de nature reversible, sont done
inapplicables aux etres vivants". "Nous pouvons rever d'equations
fonctionnelles plus compliquees que les equations classiques parce
qu 'elles renfermeront en outre des integrates prises entre un
temps passe tres eloigne et le temps actuel, qui apporteront la
part de l'heredite". (See "La mathematique dans ses rapports avec
la physique, Actes du rv* congres international des Mathematiciens,
Rome, 1908. ) Many years have passed since this publication. These
years have seen substantial progress in many aspects of Functional
Differential Equations (FDEs ). A distinguishing feature of the
FDEs under consideration is that the evolution rate of the
proc{lsses described by such equations depends on the past history.
The discipline of FDEs has grown tremendously, and publication of
literature has increased perhaps twofold over publication in the
previous decade. Several new scientific journals have been
introduced to absorb this increased productivity. These journals
reflect the broadening interests of scientists, with ever greater
attention being paid to applications.
At the beginning of this century Emil Picard wrote: "Les equations
differentielles de la mecanique classique sont telles qu 'il en
resulte que le mouvement est determine par la simple connaissance
des positions et des vitesses, c 'est-a-dire par l 'etat a un
instant donne et a ['instant infiniment voison. Les etats
anterieurs n'y intervenant pas, l'heredite y est un vain mot. L
'application de ces equations ou le passe ne se distingue pas de l
'avenir, ou les mouvements sont de nature reversible, sont done
inapplicables aux etres vivants". "Nous pouvons rever d'equations
fonctionnelles plus compliquees que les equations classiques parce
qu 'elles renfermeront en outre des integrates prises entre un
temps passe tres eloigne et le temps actuel, qui apporteront la
part de l'heredite". (See "La mathematique dans ses rapports avec
la physique, Actes du rv* congres international des Mathematiciens,
Rome, 1908. ) Many years have passed since this publication. These
years have seen substantial progress in many aspects of Functional
Differential Equations (FDEs ). A distinguishing feature of the
FDEs under consideration is that the evolution rate of the
proc{lsses described by such equations depends on the past history.
The discipline of FDEs has grown tremendously, and publication of
literature has increased perhaps twofold over publication in the
previous decade. Several new scientific journals have been
introduced to absorb this increased productivity. These journals
reflect the broadening interests of scientists, with ever greater
attention being paid to applications.
Give, and it shall be given unto you. ST. LUKE, VI, 38. The book is
based on several courses of lectures on control theory and appli
cations which were delivered by the authors for a number of years
at Moscow Electronics and Mathematics University. The book,
originally written in Rus sian, was first published by Vysshaya
Shkola (Higher School) Publishing House in Moscow in 1989. In
preparing a new edition of the book we planned to make only minor
changes in the text. However, we soon realized that we like many
scholars working in control theory had learned many new things and
had had many new insights into control theory and its applications
since the book was first published. Therefore, we rewrote the book
especially for the English edition. So, this is substantially a new
book with many new topics. The book consists of an introduction and
four parts. Part One deals with the fundamentals of modern
stability theory: general results concerning stability and
instability, sufficient conditions for the stability of linear
systems, methods for determining the stability or instability of
systems of various type, theorems on stability under random
disturbances."
This volume provides an introduction to the properties of
functional differential equations and their applications in diverse
fields such as immunology, nuclear power generation, heat transfer,
signal processing, medicine and economics. In particular, it deals
with problems and methods relating to systems having a memory
(hereditary systems). The book contains eight chapters. Chapter 1
explains where functional differential equations come from and what
sort of problems arise in applications. Chapter 2 gives a broad
introduction to the basic principle involved and deals with systems
having discrete and distributed delay. Chapters 3-5 are devoted to
stability problems for retarded, neutral and stochastic functional
differential equations. Problems of optimal control and estimation
are considered in Chapters 6-8. For applied mathematicians,
engineers, and physicists whose work involves mathematical modeling
of hereditary systems. This volume can also be recommended as a
supplementary text for graduate students who wish to become better
acquainted with the properties and applications of functional
differential equations.
'E.t moi, .. " si j'avait su comment en revenir, One service
mathematics has rendered the human race. It has put common sense
back je n'y serais point aile.' Jules Verne where it belongs, on
the topmost shelf nex t to the dusty canister labelled 'discarded
non- The series is divergent; thererore we may be sense'. able to
do something with it. Eric T. Bell O. Heaviside Mathematics is a
tool for thought. A highly necessary tool in a world where both
feedback and non linearities abound. Similarly, all kinds of parts
of mathematics serve as tools for other parts and for other
sciences. Applying a simple rewriting rule to the quote on the
right above one finds such statements as: 'One service topology has
rendered mathematical physics .. .'; 'One service logic has
rendered com puter science .. .'; 'One service category theory has
rendered mathematics .. .'. All arguably true. And all statements
obtainable this way form part of the raison d'etre of this series."
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