Observer based self-triggered control of an acyclic interconnection of linear plants

This paper addresses the control of linear time-invariant plants whose dynamics are interconnected in an acyclic manner and are subject to unknown disturbances. Moreover, each plant's output is only measured at sampling instants determined by a self-triggered strategy. In a self-triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on a priori knowledge about the plant and on an estimate of the plant's state. We first address the single plant case where the proposed solution is a cascade interconnection of a state observer and a self-triggered controller designed for state feedback. We then consider the case where several plants are interconnected in an acyclic manner. In both cases, it is shown that the closed-loop system is input-to-state stable with respect to all bounded exogenous disturbances.