Minimization of the L/sup infinity /-induced norm for sampled-data systems

It is shown that given any degree of accuracy, there exists a standard discrete-time l/sup 1/ problem that can be determined a priori whose solution yields a controller that is almost optimal in terms of the hybrid L/sup infinity /-induced norm. This is accomplished by first converting the hybrid system into an equivalent infinite-dimensional discrete-time system using the lifting technique in continuous time, and then approximating the infinite-dimensional parts of the system which model the intersample dynamics. A thorough analysis of the approximation procedure is presented, and it is shown that it is convergent at the rate of 1/n. Explicit bounds that are independent of the controller are obtained to characterize the approximation. It is also shown that the geometry of the induced norm for the sampled-data problem is different from that of the standard l/sup 1/ norm, and hence there might not exist a linear isometry that maps the sampled-data problem exactly to a standard discrete-time problem.<
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