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 infinite-dimensional distributed parameter systems (DPS) is not always guaranteed. We introduce two nonlinear controllers, a DPS one and a finite-dimensional one with residual mode filter 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