The synthesis of a feedforward unit for $H_2$ optimal decoupling of measurable or previewed signals in discrete-time linear time-invariant systems is considered. It is shown that an $H_2$ optimal compensator can be achieved by connecting a finite impulse response (FIR) system and a stable dynamic unit. To derive the FIR system convolution profiles an easily implementable computational scheme based on pseudoinversion (possibly nested to avoid computational constraints) is proposed, while the dynamic unit...

In this paper we first present a full order $H_{\infty }$ controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order $H_{\infty }$ controller and demonstrate that the closed-loop (CL) system with the reduced order $H_{\infty }$ controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order $H_{\infty }$ controller it is found that the dynamical behavior of the reduced order $H_{\infty }$ controller can be accurately approximated by...

In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task....