Mixed H2/H∞ control for stochastic continuous-time systems with input delay

This paper is concerned with the mixed H
2
/H
∞
control for stochastic continuous time systems with input delay. Using the method of Stackelberg strategy, the control strategy is to minimize the cost function of H
2
norm, while the disturbance is to maximize the cost function of H
∞
norm. This paper overcomes the difficulties in dealing with both the stochastic Brownian motion and the input delay, using ${\text{It}}\hat o$ formula based on the stochastic maximum principle and introducing new states. The open-loop strategy of the system is obtained by solving several Riccati equations.