H∞ finite memory controls for linear discrete-time systems

In this paper, we propose output-feedback finite memory controls (FMC) for a H_∞ criterion. Unlike conventional infinite memory controls with internal states, the proposed FMC is required to utilize only inputs and outputs on the recent finite time instead of using an internal state involved with old data. The H_∞ criterion is employed to obtain FMCs robust to uncertain disturbances. An augmented model with the FMC and a system is first constructed and then the optimization problems are represented with bilinear matrix inequalities (BMI) to solve numerically. Using the cone-complementarity linearization (CCL) algorithm, we provide a numerical solution. It was shown in a numerical example that the proposed FMC has better performance than other controls including static controls and infinite memory controls.