Low order sampled data H∞ control using the delta operator and LMIs

A procedure for H_∞ optimization of low order controllers for discrete-time and sampled-data systems is presented in this paper. Generally, low order H_∞ controllers may be achieved by solving bilinear matrix inequalities (BMIs). In this paper an iterative alternation between two LMIs gives a suboptimal solution. To avoid local minima in this search the initial controller is obtained by a frequency weighted controller reduction scheme, where the closed loop properties of a full order controller is taken into account. A minimal number of parameters in the state space realization of the controller also reduces the complexity and improves numerical robustness. The complete presentation is based on delta operator models, which shows a close relationship between the continuous- and discrete-time solutions. The sensitivity of the ordinary discrete-time shift operator LMI formulation to small sampling periods is also analyzed.