Description The book describes a new application of Liapunov matrix-valued functions method to the stability of evolution problems governed by nonlinear continuous systems, discrete time systems, impulsive systems and singularly perturbed systems. The authors take a challenging and original approach based on the concept of structural perturbations combined with direct Liapunov’s method. The book is intended for specialists in dynamical systems, applied differential equations, and the stability theory. it may also be useful for graduate students and researchers in mathematics, control theory, and mechanical engineering.