H∞ Closed–Loop Control for Unstable Uncertain Discrete Input–Shaped Systems

This article focuses on the design of a discrete robust H∞ controller for an input–shaped, underdamped, (stable or unstable) system. The system is noiseless, uncertain, time– invariant and its characteristic polynomial coefficients are allowed to vary within predefined interval–sets. A discrete input shaper is used for the nominal system generating a pre– compensated discrete Finite Impulse Response shaped system. The shaped system’s description is reformulated in order to be amenable to a robust controller synthesis. The designed H∞ controller compensates for the uncertainties of the system’s parameters while providing the control command for stabilizing the system.