${\cal H}_{\infty}$ Finite Memory Controls for Linear Discrete-Time State-Space Models

In this brief, we propose a new type of output feedback control, called a ${\cal H}_{\infty }$ finite memory control (HFMC), for discrete-time state-space systems. Some constraints, such as linearity, unbiasedness to the optimal state feedback control, and finite memory structure with respect to an input and an output are required in advance. Among the controls needed with these requirements, we choose the HFMC to optimize the ${\cal H}_{\infty}$ performance criterion. The HFMC is obtained by solving the linear matrix inequality problem with a parameterization of a linear equality constraint. We show through simulation that the HFMC is more robust against uncertainties, and is faster in convergence than existing ${\cal H}_{\infty}$ output feedback controls.