Robust stability bounds for sampled-data systems

Abstract

Abstract This paper is concerned with the robust stability of sampled-data systems whose underlying continuous-time system is subjected to additive parameter perturbations. In particular, the process by which parameter perturbations in the underlying continuous-time model are propagated into the discrete-time one is examined, and upper bounds on these induced perturbations are proposed. In addition robust stability bounds for discrete-time systems are derived. Combining the above findings yields new robust stability bounds on the underlying continuous-time perturbations. Owing to the exponential-like structure of the induced perturbations, relatively computationally demanding implicit bounds, are derived for structured perturbations. It is shown in the paper that the sampling rate is a crucial design parameter when it comes to reducing the effect of the perturbations. Examples are given to illustrate the proposed results.