Exponentially Stable Feedback Control of Discrete-Time Nonlinear Distributed Parameter Systems on Banach Spaces

Practical engineering systems require feedback control implementation in discrete-time; however, stable control of an infinite-dimensional distributed param- eter system DPS.is not always guaranteed. We introduce two nonlinear con- trollers, a DPS one and a finite-dimensional one with residual mode filter RMF. compensation, which produce local exponential closed-loop stability for nonlinear discrete-time DPS on Banach spaces under appropriate local Lipschitz continuity conditions. Both controllers operate in discrete-time and our results place no restrictions on the smoothness of the initial data in the Banach space.