Book

Description

The analytical stability of time-varying systems has attracted the attention of many researchers and has produced a large body of important results. The main goal of developing the theory of stability is to examine the dynamic responses of a system to disturbances as time approaches infinity. It has been and still the subject of intense investigation due to its interest in its relevance to all practical systems in technology, finance, natural science and social science. The subject of this book is around the stability and stabilization of certain nonlinear systems by introducing a new notion of convergence called: h-stability and practical h-stability. We have dealt with several questions around h-stability and characterize this notion by being able to provide a converse theorem which has made it possible to study perturbed systems. Further, we have given new sufficient conditions to ensure the asymptotic behavior of solutions of certain classes of dynamical systems, using Lyapunov techniques and Gronwall ‘s inequalities. In addition, the local case is also characterized and we studied the h-stabilization problem by constructing a state feedback controller for a class of nonlinear systems in the presence of a perturbed term.