Enhancing data-driven control for sampled-data systems with polytopic disturbances

This paper advances data-driven control techniques for linear sampled-data systems subject to process disturbances in the data. It introduces a matrix-polytopic data-based system representation, modeling the disturbance as a convex polytopic constraint, which offers increased consistency with the noise data compared to existing methods in the case of pointwise-in-time ∞-norm bounded noise. Furthermore, the paper proposes a combination-type extended looped-functional (cELF) approach, enabling more flexible stability conditions that do not necessitate positive definiteness and continuity at sampling points. By integrating cELF with the matrix-polytopic data-based representation, the paper derives a fresh data-based stability criterion expressed as linear matrix inequalities (LMIs), enhancing the effectiveness of data-driven control design. Numerical examples demonstrate that the proposed model- and data-based conditions allow for larger maximum sampling intervals (MSIs) than existing results, ensuring stability under designed controllers.