Sets and Stability Domains

The book establishes a unified stability theory for general time-varying nonlinear systems, based on the consistent stability methodology. This theoretical work broadens and generalizes stability theory beyond the existing Lyapunov stability framework, permitting the dependence of stability properties on the initial instant of the system. The book establishes a unified stability theory for general time-varying nonlinear systems, based on the consistent stability methodology. This theoretical work broadens and generalizes stability theory beyond the existing Lyapunov stability framework, permitting the dependence of stability properties on the initial instant of the system. The book focuses on the stability domains of positive invariant sets, which can include equilibrium states, limit cycles, or any positive invariant set of the system. Contributes new concepts, definitions of sets and system features Aims to open new directions for research in the stability theory as an essential introduction to the tracking theory and enables new various engineering applications. Includes time-varying and nonlinear nature of the systems which ensures the generality of the concepts, definitions, conditions and criteria This book is aimed towards professors, researchers, engineers and advanced students in mathematics, physics, dynamical systems science, control science and engineering.