Linear quadratic Nash differential games of stochastic singular systems with Markovian Jumps

Abstract

This paper investigates Nash games for stochastic singular systems with Markovian jumps. Based on the generalized Itô’s formula, the corresponding linear quadratic optimal control problem is studied for the first time. Then, we establish the existence of Nash strategies by- means of generalized coupled Riccati algebraic equations. As an application, the stochastic H₂ / H∞ control with state, control, and external disturbance-dependent noise is discussed.