Laila, Dina Shona, Nesic, Dragan and Teel, Andrew
Open and closed loop dissipation inequalities under sampling and controller emulation
European Journal of Control, 8, (2), . (doi:10.3166/ejc.8.109-125).
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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