Sampled-Data Output Feedback Control of Distributed Parameter Systems via Semi-discretization in Space

Abstract

This paper provides sufficient conditions to stabilize a sampled-data linear distributed parameter system with finite-dimensional input and output via a family of finite-dimensional approximations that are obtained from numerical schemes. This family of finite-dimensional approximations can be exponentially stabilized by a family of output feedback controllers when the space discretization parameter h is sufficiently small. The sufficient conditions presented in this paper guarantee that the same family of output feedback controllers can exponentially stabilize the exact sampled-data linear distributed parameter system for a sufficiently small sampling period. Since the output feedback controller design is based on the family of finite-dimensional approximations which only require a standard finite-dimensional control theory, this result can simplify the design of controller for sampled-data infinite-dimensional systems when the sampling period is fast enough and those sufficient conditions are satisfied. Moreover, the analysis method is applicable to more general situations when the sampled-data state feedback controllers are designed based on finite-dimensional approximations.