In the present book the problems of stability and non-stability of dynamical systems are considered, systems with declining argument and systems with distributive parameters when the system at the end of the time interval is affected by integrally small perturbation forces. The problems of stabilization and optimal stabilization of such systems are also considered. A new definition is given to stability, that is: "stability with integrally small perturbations". Besides, these perturbation forces, defined at the final interval of time, are chosen from the class of generalized functions (they can be impulsive functions).