The sampled-data H∞ problem: the equivalence of discretization-based methods and a Riccati equation solution

For the solution of the sampled-data H_∞ problem various approaches have been introduced. A commonly used method is the lifting procedure, in which the problem is transformed into an equivalent discrete-time H_∞ problem, which can be solved by standard methods. An alternative approach is to consider the sampled-data system as a periodically time-varying system, and to solve the problem directly by applying H_∞ control theory of time-varying systems. This method gives the solution in terms of two coupled Riccati differential equations with jumps. The purpose of this paper is to show that the two methods are indeed closely connected, and to show explicitly that the procedures give identical synthesis equations for the sampled-data H_∞-optimal controller