Recursive Stochastic H2/H∞ Control Problem for Delay Systems Involving Continuous and Impulse Controls

In this paper, we discuss the recursive stochastic H₂/H_∞ control problem of delay systems with random coefficients involving both continuous and impulse controls. By virtue of a new type of forward backward stochastic differential equations, a necessary and sufficient condition for the existence of a unique solution to the control problem under consideration is derived. The existence and uniqueness of the forward backward stochastic differential equations are also be proved.