Stabilizing solutions to coupled matrix Riccati differential equations associated to linear systems with Markovian jumping and multiplicative noise

In this paper the existence of global solutions to game theoretic Riccati differential equations related to the disturbance attenuation probem associated to the linear controlled systems with Markovian jumping and multiplicative white noise is investigated. One proves that if a stabilizing and attenuating feedback exists then a system of matrix differential game-theoretic Riccati equations has a unique global bounded stabilizing positive semidefinite solution; this solution is periodic if the coefficients are periodic functions and it solves a system of algebraic Riccati equations if the coefficients are constant. Conversly, if such a solution exists it allows an explicit construction of a robustly stabilizing feedback gain.