Robust H _∞ controller design for sampled-data systems with parametric uncertainties

This article investigates the problem of robust H _∞ controller design for sampled-data systems with time-varying norm-bounded parameter uncertainties in the state matrices. Attention is focused on the design of a causal sampled-data controller, which guarantees the asymptotical stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed H _∞ performance bound for all admissible uncertainties. Sufficient condition for the solvability of the problem is established in terms of linear matrix inequalities (LMIs). It is shown that the desired H _∞ controller can be constructed by solving certain LMIs. An illustrative example is given to demonstrate the effectiveness of the proposed method.