On the Stabilizing Solution of Periodic Riccati Differential Equations Related to a Class of Stochastic Linear Quadratic Differential Game

摘要

We consider a two players linear quadratic differential game associated to a positive θ-periodic dynamical system with jump Markov perturbations. We introduce the concept of stabilizing solution and strong stabilizing solution of the associated system of coupled matrix Riccati differential equations and we will point out the relation between these kinds of solutions. Moreover, we provide a set of conditions which guarantee the existence of strong stabilizing and θ-periodic solution (stabilizing and θ-periodic solution, respectively) of the considered set of coupled matrix Riccati differential equations.