H∞ Control of Discrete-Time Systems With Multiple Input Delays

This paper is concerned with the finite horizon H_infin full-information control for discrete-time systems with multiple control and exogenous input delays. We first establish a duality between the H_infin full-information control and the H₂ smoothing of a stochastic backward system in Krein space. Like the duality between the linear quadratic regulation (LQR) of linear systems without delays and the Kalman filtering, the established duality allows us to address complicated multiple input delay problems in a simple way. Indeed, by applying innovation analysis and standard projection in Krein space, in this paper we derive conditions under which the H_infin full-information control is solvable. An explicit controller is constructed in terms of two standard Riccati difference equations of the same order as the original plant (ignoring the delays). As special cases, solutions to the H_infin state feedback control problem for systems with delays only in control inputs and the H_infin control with preview are obtained. An example is given to demonstrate the effectiveness of the proposed H_infin control design