A Nash Game Approach to Mixed H2/ H∞ Problem with Input Delay: The Discrete-time Case

As an important branch of control theory, mixed
$H$
2
/
$H$
∞
control can not only enable the system to obtain excellent regulation characteristics but also maintain robust stability, which has important theoretical significance and extensive application background. This paper studies mixed H
2
/ H
∞
problem with input delay. The mixed H
2
/ H
∞
control problem can be equivalently described as the LQ non-zero sum game problem, namely, Nash game problem. Based on Nash game strategy, the optimal solution for discrete time system with input delay is given. The maximum principle is established, by solving the delayed forward backward difference equations, sufficient and necessary conditions of solvability are obtained.