H_∞ Estimation of Nonlinear Time-Varying Systems with Data Packet Dropouts

This paper handles the finite-horizon state estimator design issue for nonlinear time-varying systems under the effect of multiplicative noise and random data packet dropouts. Stochastic nonlinear function with known statistical properties is employed to depict the nonlinear intrinsic characteristics of real systems. The phenomenon of random data packet dropouts is characterized using a random variable following the Bernoulli distribution. Multiplicative noise is incorporated as well as additive process noise. Through the utilization of stochastic analysis, matrix computation and completing squares approach, a necessary and sufficient condition is proposed to ensure the existence of ideal estimators that satisfy the performance requirement. The time-varying gain parameters of the estimators are derived by recursively solving a group of coupled backward Riccati difference equations. Correctness of the developed estimation approach is verified via a simulation example.