On preservation of dissipation inequalities under sampling

Nesic, Dragan, Laila, Dina Shona and Teel, Andrew (2000) On preservation of dissipation inequalities under sampling. In Proceedings of the 39th IEEE Conference on Decision and Control, 2000. IEEE. pp. 2472-2477 . (doi:10.1109/CDC.2000.914173).

Record type: Conference or Workshop Item (Paper)

Abstract

We show that if we first design a controller for a continuous-time nonlinear plant with disturbances so that it achieves a certain dissipation inequality for the continuous-time closed-loop system and then implement it as a sampled-data controller using a sampler and zero order hold, then the dissipation inequality will be preserved for the exact discrete-time model of the sampled data closed-loop system in a semiglobal practical sense (the sampling period is the parameter that we can adjust). Moreover, a similar statement is proved for open-loop systems, where controls are considered as free variables. Two different forms of dissipation inequalities are considered for the exact discrete-time models: the “weak” form and the “strong” form

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