Linear differential games with impulse action and fixed termination time (Q2755256)

This article deals with differential games described by the equation with an impulse action \(\dot z=Az+B(u,v)\), \(\Delta z|_{t=\tau}=\Gamma_{\tau}z-z\), where \(z\in E^{n}\); \(u\in U\), \(v\in V\) are the players control parameters; \(U, V\) are compacts; \(A:E^{n}\to E^{n}\) is a linear operator; \(B: U\times V\to E^{n}\) is a continuous function; \(\Gamma_{\tau}=Gz+l\), \(G\) is a matrix; \(l\) is a vector. A closed terminal set \(M\) and a closed set of phase constraints \(N\) are given. The author describes the class of games for which it is possible to construct the player strategy and the set of favourable initial positions for each player.