H2 and H∞ design of sampled-data systems using lifting.: part I:: General framework and solutions

This paper presents a complete solution to the H-2 and H-infinity problems for sampled-data systems. As opposed to previous works in the area, it is assumed here that all or some of the sampling function, the discrete-time controller, and the hold function are available for design. The solution is obtained by transforming the problem to discrete time using the well-known lifting technique. It is then shown that the desired components of the sampled-data controller can be "peeled-off" from the inherently infinite-dimensional description in the lifted-domain. The procedure for doing this last step is central to the approach in this paper. Both new and revised solutions are presented in this paper. The solution to the H-2 problems is completely new. The solution to the H-infinity problems is presented in a unifying framework and is more transparent than the previous existing solutions in the literature. Transparency pays in the form of clearer results. In particular, a separation structure is established between the design of (sub)optimal hold and sampler.