Linear and Nonlinear Event-Triggered Extended State Observers for Uncertain Random Systems

In this paper, linear and nonlinear event-triggered extended state observers are designed for a class of uncertain random systems driven by bounded noise and colored noise. Two event-generators with an ensured positive minimum inter-event time for every sample path solution of the random systems, are proposed for the designs of linear and nonlinear event-triggered extended state observers, respectively. The mean square and almost sure convergence of the estimation errors of unmeasured state and random total disturbance including internal uncertainty and external random noises is presented with rigorous theoretical proofs. Compared with the linear event-triggered extended state observer, the theoretical results show that the nonlinear one via homogeneity possesses higher estimation accuracy but is at the price of higher triggering frequency. Some numerical simulations are performed to authenticate the theoretical results.