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Observer-Based Event-Triggered Control for Nonlinear Systems With Mixed Delays and Disturbances: The Input-to-State Stability

In this paper, the input-to-state stabilization problem is investigated for a class of nonlinear delayed systems with exogenous disturbances. The model under consideration is general that covers for both mixed time-delays and Lipschitz-type nonlinearities. An observer-based controller is designed such that the closed-loop system is stable under an event-triggered mechanism. Two separate event-triggered strategies are proposed in sensor-to-observer (S/O) and controller-to-actuator (C/A) channels, respectively, in order to reduce the updating frequencies of the sensor and the controller with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to characterize the performance of the controlled system that caters for the influence from both disturbances and event-triggered schemes. The estimates of the upper bounds of the delayed states and two measurement errors are employed to analyze and further exclude the Zeno behavior resulting from the proposed event-triggered schemes in S/O and C/A channels. The controller gain matrices and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.