A local approach to the inverse minimax control problem for discrete-time systems

A local approach based on Lyapunov function technique is used to discuss both the direct and the inverse problems of minimax control for linear discrete-time systems. Based on a proposed solution to the inverse problem of worst-case disturbance, the necessary and sufficient conditions are derived, under which a given locally worst-case disturbance and a given locally minimax control will be the worst-case disturbance and the minimax control, respectively, for some quadratic performance index with a suitable nonnegative weight on the state. It is also shown that the set of all linear state feedbacks corresponding to minimax controls is a subset of the set of all stable feedbacks corresponding to optimal controls in the absence of disturbances