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Observer based self-triggered control of linear plants with unknown disturbances

This paper addresses the control of linear time-invariant plants in the presence of unknown disturbances when the plant's output is only measured at sampling instants determined by a self-triggering strategy. In a self-triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on available measurements and on a priori knowledge about the plant. The proposed solution is a cascade interconnection of a discrete time observer and a self-triggered controller designed for state feedback. We focus our attention on discrete-time observers that are input-to-state stable (ISS) with respect to disturbances for all possible sequences of sampling times. Self-triggered control strategies presented in the literature are known to be ISS with respect to observation errors and exogenous disturbances. Due to the cascade structure of the closed-loop system, we conclude that the closed-loop is rendered ISS with respect to all bounded exogenous disturbances.