H-2 and H-infinity 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 a ssumed here that all or some of the sampling function, the discrete-time co ntroller, 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 compon ents of the sampled-data controller can be "peeled-off" from the inherently infinite-dimensional description in the lifted-domain. The procedure for d oing 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 problem s is presented in a unifying framework and is more transparent than the pre vious existing solutions in the literature. Transparency pays in the form o f clearer results. In particular, a separation structure is established bet ween the design of (sub)optimal hold and sampler.