Variance-Constrained ${\cal H}_{\infty}$ Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements: The Finite-Horizon Case

This paper is concerned with the robust
H

_∞
finite-horizon filtering problem for a class of uncertain nonlinear discrete time-varying stochastic systems with multiple missing measurements and error variance constraints. All the system parameters are time-varying and the uncertainty enters into the state matrix. The measurement missing phenomenon occurs in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval . The stochastic nonlinearities under consideration here are described by statistical means which can cover several classes of well-studied nonlinearities. Sufficient conditions are derived for a finite-horizon filter to satisfy both the estimation error variance constraints and the prescribed
H

_∞
performance requirement. These conditions are expressed in terms of the feasibility of a series of recursive linear matrix inequalities (RLMIs). Simulation results demonstrate the effectiveness of the developed filter design scheme.