We present a general and unified framework for the design of nonlinear digital controllers using the emulation method for nonlinear systems with disturbances. It is shown that if a (dynamic) continuous-time controller, which is designed so that the continuous-time closed-loop system satisfies a certain dissipation inequality, is appropriately discretized and implemented using sample and zero-order-hold, then the discrete-time model of the closed-loop sampled-data system satisfies a similar dissipation inequality in a semiglobal practical sense (sampling period is the parameter that we can adjust). We consider two different forms of dissipation inequalities for the discrete-time model: the “weak” form and the “strong” form. The results are also applicable for open-loop systems.
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- Emulation Design
Laila, D. S., Nešić, D., & Teel, A. R. (2002). Open- and Closed-Loop Dissipation Inequalities Under Sampling and Controller Emulation. European Journal of Control, 8(2), 109-125. https://doi.org/10.3166/ejc.8.109-125