Sufficient Conditions for Stabilization of Sampled-data Linear Spatially Distributed Parameter Systems via Discrete time Approximations

In this paper we present preliminary results on sampled-data controller design for linear spatially distributed parameter systems (SDPS) via their discrete time approximations. Analogous to the results on sampled-data control of linear/nonlinear lumped parameter systems (LPS), we show that exponential stability of an approximate discrete time model implies exponential stability of the original sampled-data linear SDPS, provided that an appropriate consistency condition holds between the exact and approximate closed-loop systems. Consequently, the controller can be designed on the basis of an approximate discrete time model.