RATIONAL LAMBDA-1 SUBOPTIMAL COMPENSATORS FOR CONTINUOUS-TIME SYSTEMS

The persistent disturbance rejection problem (L1 optimal control) for continuous time-systems leads to nonrational compensators, even for si ngle input/single output systems [1]-[3]. As noted in [2], the difficu lty of physically implementing these controllers suggest that the most significant application of the continuous time L1 theory is to furnis h achievable performance bounds for rational controllers. In this pape r we use the theory of positively invariant sets to provide a design p rocedure, based upon the use of the discrete Euler approximating syste m, for suboptimal rational L1 controllers with a guaranteed cost. The main results of the paper show that i) the L1 norm of a continuous-tim e system is bounded above by the L1 norm of an auxiliary discrete-time system obtained by using the transformation z = 1 + taus and ii) the proposed rational compensators yield L1 cost arbitrarily close to the optimum, even in cases where the design procedure proposed in [2] fail s due to the existence of plant zeros on the stability boundary.