Linear quadratic regulation for systems with time-varying delay

In this paper we study the linear quadratic regulation (LQR) problem for discrete-time systems with time- varying delay in the control input channel. We assume that the time-varying delay is of a known upper bound. The LQR problem is first converted to the optimal control problem for an associated system with multiple input channels, each of which has single constant delay. The optimal controller is then derived by establishing a duality between the LQR and a smoothing estimation for a stochastic backward system whose measurement is of a special form of multiple state delays.