Matrix resolving functions in game dynamic problems

The paper concerns conflict-controlled processes of general kind with cylindrical terminal set. Solutions of a dynamic system are presented in a general form, encompassing, in particular, processes with various-type fractional derivatives, impulse processes, and systems of integral, integro-differential and difference-differential equations. Ideas of the method of resolving functions are used as a basis for investigation. While scalar resolving functions execute attraction of sets to the origin, the matrix functions introduced in the paper also admit rotation through any angle, that essentially extends the scope of the method applications. Sufficient conditions for the game termination in a guaranteed time in the class of quasi- and stroboscopic strategies are developed.