FIR-type state-feedback control law for discrete-time LTI systems with polytopic uncertainties

Recently, the so-called FIR-type (FIR, finite impulse response) state-feedback memory controller and periodic memory controller have been developed, and it was revealed that this control design approach can reduce the conservatism of stability and stabilization conditions for periodic or uncertain systems. In these work, the system duality and a descriptor representation of the original system are used. In this paper, we focus only on the FIRtype state-feedback memory controller design problem, which is a special case of the general memory controller structure previously developed. Although the structure of the controller considered in this paper is a particular case of the existing one, this special consideration gives some benefits, which are the main purpose of this paper. Finally, examples demonstrate the effectiveness of the FIR-type state-feedback memory controller in terms of less conservatism.