Springer Science & Business Media, Mar 2, 2009 - Science - 461 pages
"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student."
—The Journal of the Indian Institute of Science
"The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. It includes...results with many historical comments giving the reader a sound perspective to look at the subject...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis."
"I recommend this book as one to dig into with considerable pleasure when one already knows the subject...‘Set-Valued Analysis’ goes a long way toward providing a much needed basic resource on the subject."
—Bulletin of the American Mathematical Society
"This book provides a thorough introduction to multivalued or set-valued analysis...Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and set-valued maps...The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis."
Results 1-5 of 26
... 379 10 Differential Inclusions 383 10.1 The Viability Theorem 387 10.1.1 Solutions to Differential Inclusions 388 ... 10.2.1 Linear Differential Inclusions 395 10.2.2 Lyapunov Functions 395 10.2.3 Tracking a Differential Inclusion ...
So, the control system governed by the family of parametrized differential equations x'(t) = f(x(t),u(t)) where u(t) € U(x(t)) is actually governed by the differential inclusion x'(t) 6 F(x(t)) 6. Optimization provides examples of ...
Nonlinear Functional Analysis We are convinced that many problems can be regarded as inclusions given F : X ~> Y and ... the derivatives of the maps Fn . This provides a first motivation for devising a set-valued differential calculus.
The idea is very simple and goes back to the prehistory of the differential calculus, when Pierre de Fermat ... we study the monotone behavior of a function along a solution to a differential equation or inclusion (Lyapunov property.) ...
Another important instance where measurable set- valued maps do arise is in the linearization of a control system (or a differential inclusion) along a solution. Hence, we cannot escape the burden of studying measurable maps, ...