A linear matrix inequality (LMI) approach to robust H2 sampled-data control for linear uncertain systems

In this paper, we consider the H-2 sampled-data control for uncertain linear systems by the impulse response interpretation of the H-2 norm. Two H-2 measures for sampled-data systems are considered. The robust optimal control procedures subject to these two H-2 criteria are proposed. The development is primarily concerned with a multirate treatment in which a periodic time-varying robust optimal control for uncertain linear systems is presented. To facilitate multirate control design, a new result of stability of hybrid system is established. Moreover, the single-rate case is also obtained as a special case. The sampling period is explicitly involved in the result which is superior to traditional methods. The solution procedures proposed in this paper are formulated as an optimization problem subject to linear matrix inequalities. Finally, we present a numerical example to demonstrate the proposed techniques.