A Treatise on Stability of Autonomous and Non-autonomous Systems

By a stable dynamical system, we broadly mean the one whose overall behavior does not substantially change when its initial conditions or inputs undergo small disturbances. Stability is the fundamental requirement of any practically useful system. The behavior of an unstable system cannot be controlled and hence such a system is simply useless for practical purpose. The aim of this book is to present a concise study of the stability theories of autonomous (time-invariant) and non-autonomous (time-varying) systems. Various related notions and terminologies are meticulously explained. A major focus of the book is on the celebrated Liapunov s direct method which is so far the best mathematical technique for determining the stability nature of a dynamical system. The book introduces and lucidly discusses about the theory of stability of non-autonomous systems which is a complicated subject, having various pitfalls and peculiarities. All concepts in the book are accompanied with illustrative mathematical examples, selected from standard books and journals.

Autorentext

Ratnadip Adhikari completed M.Sc (Applied Maths) in 2006 from IIT Roorkee and M.Tech (Comp Sc & Technology) in 2009 from JNU, New Delhi. He received Gold Medal for being the Best Graduate in B.Sc (Maths Hons). His research interests include time series analysis, stability theory, data stream management and evolutionary optimization.