On a solution to the problem of time-varying zero-sum LQ stochastic difference game: A Riccati equation approach

We consider in this paper the problem of a zero-sum two players linear quadratic (LQ) difference game for a stochastic discrete-time dynamical system subject to both random switching of its coefficients and multiplicative noise. Two kinds of admissible strategies are discussed. Following a Riccati equation approach, we show that in the solution of such a control problem, a crucial role is played by the stabilizing solution of an adequately defined class of coupled Riccati difference equations. For each type of admissible strategy the specific sign properties of the stabilizing solution of the involved Riccati equations are emphasized. The solution to this problem is given in a closed form.