Design of \(H_2\) controllers for sampled-data systems with input time delays (Q1770585)

Linear time invariant sampled-data systems are considered in this paper. It is assumed that the input of the systems is delayed by a constant time delay. Therefore within one sampling interval two different values of the input sequence are applied to the system. The influence of the control input sequence on the output can be described by two lifted systems. With lifting techniques sampled data systems are converted into time invariant discrete time infinite dimensional systems. A generalized \(H_2\) measure is introduced. A method for designing discrete time controllers such that \(H_2\) norm is optimized is presented. A MATLAB function can be used for optimization. The method is illustrated by a numerical example. Simulation results are presented.