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STUDIA MATHEMATICA - Issue no. 4 / 2009 | |||||||
Article: |
BOOK REVIEWS: WASSIM M. HADDAD AND VIJAY SEKHAR CHELLABOINA, NONLINEAR DYNAMICAL SYSTEMS AND CONTROL, A LYAPUNOV-BASED APPROACH, PRINCETON UNIVERSITY PRESS, PRINCETON AND OXFORD 2008, XVI+948 PP. Authors: MARCEL-ADRIAN ŞERBAN. |
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Abstract: The book under review is a graduate-level textbook which presents and develop an extensive treatment of stability analysis and control design of nonlinear dynamical systems using the Lyapunov methods. The book is structured in 14 chapters. The authors introduce the definition of dynamical systems and present a systematic development of the theory of nonlinear differential equations. There are presented the qualitative theory of existence, uniqueness, continuous dependence of solutions on the initial conditions for nonlinear differential equations, the stability theory for nonlinear dynamical systems generated by these nonlinear differential equations, Lyapunov stability theorems for time-invariant nonlinear dynamical systems, invariant set stability theorems, converse Lyapunov theorems and Lyapunov instability theorems. | |||||||