H∞ Control for Discrete-time System with Input Time-varying Delay

This paper is concerned with the finite horizon H∞ control for discrete-time systems with time-varying delay in control and exogenous input channels. By defining a binary variable, the problem is first transformed into the one with multiple input channels, each of which has a constant delay. Then, the problem is solved by using the duality principle between the H∞ control problem and smoothing estimation problem for an associated system without delays. The solution is given in terms of one standard Riccati difference equation (RDE) of the same order as the original system.