Ostapenko O. Differential games with dynamics, which is exposed by impulse influence

Thesis is devoted to research of differential games, which dynamics is exposed by impulse influence in fixed instants and under hit on some subset of a phase space. The games with fixed time of a termination and terminal set, with terminal function of the payment and with dynamics " simple moving " are considered. For nonlinear cases the structures of games are described and the theorems of alternative are proved. The concept of matrix convexity for sets of operators was coined and investigated. The classes of games which for is possible to construct the effective strategies of the players are circumscribed for linear cases with the help of concepts H - the convexities and matrix convexity.