Linear matrix inequality-based robust H_∞ control of sampled-data systems with parametric uncertainties

The problem of robust H_∞ controller design for sampled-data systems with time-varying norm-bounded parameter uncertainties in the state matrices is investigated. 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 in terms of linear matrix inequalities (LMIs) technique. 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.