Mixed H2/H∞ Finite Memory Controls for Output Feedback Controls of Discrete-time State-Space Systems

In this paper, a new type of output feedback control, called a H2/H∞ finite memory control (FMC), is proposed for deterministic state space systems. Constraints such as linearity, unbiasedness property, and finite memory structure with respect to an input and an output are required in advance to design H2/H∞ FMC in addition to the performance criteria in both H2 and H∞ sense. It is shown that H2, H∞, and mixed H2/H∞ FMC design problems can be converted into convex programming problems written in terms of linear matrix inequalities (LMIs) with some linear equality constraints. Through simulation study, it is illustrated that the proposed H2/H∞ FMC is more robust against uncertainties and faster in convergence than the existing H2/H∞ output feedback control schemes.