FURTHER RESULTS ON RATIONAL-APPROXIMATIONS OF L(1) OPTIMAL CONTROLLERS

The continuous-time persistent disturbance rejection problem (L(1) opt imal control) leads to nonrational compensators, even for SISO systems [4], [7], [8]. As noted in [4], the difficulty of physically implemen ting these controllers suggest that the most significant applications of the continuous time L(1) theory is to furnish bounds for the achiev able performance of the plant. Recently, two different rational approx imations of the optimal L(1) controller were developed by Ohta ct al. [6] and by Blanchini and Sznaier [1]. In this paper we explore the con nections between these two approximations. The main result of the pape r shoes that both approximations belong to the same subset Ohm(T) Of t he set of rational approximations, and that the method proposed in [1] gives the best approximation, in the sense of providing the tightest upper bound of the approximation error, among the elements of this sub set. Additionally, we exploit the structure of the dual to the L(1) op timal control problem to obtain rational approximations with approxima tion error smaller than a prespecified bound.