This reference/text presents new approaches to qualitative analysis of continuous, discrete-time, and impulsive nonlinear systems via Liapunov matrix-valued functions that introduce more effective tests for solving problems of estimating the domains of asymptotic stability-providing a survey of results on scalar and vector functions. Enriched with over 1300 mathematical expressions. Qualitative Methods in Nonlinear Dynamics discusses innovative methods of initial system decomposition.focuses on exponential polystability of separable motions as well as integral and Lipschitz stabilities.considers problems of dynamics of nonlinear systems in the presence of impulsive perturbations.outlines the comparison principle and advantages of cone-valued Liapunov functions.details dynamics of systems with mixed and regular hierarchy subsystems.examines uniqueness, continuability, and boundedness of solutions.

highlights connective stability tests.and more. Book jacket.