Envelope-constrained ℋ∞ filtering with missing measurements

In this paper, the envelope-constrained ℋ_∞ filtering problem is investigated for a class of discrete time-varying stochastic systems with missing measurements. A sequence of random variables obeying a Bernoulli distribution is utilized to govern the phenomenon of missing measurements. A modified envelope-constrained performance criterion is proposed to better describe the transient dynamics of the filtering error process. The purpose of the problem addressed is to design a time-varying filter such that the given ℋ_∞ performance and the desired envelope-constrained requirements are guaranteed simultaneously over a finite-horizon. By utilizing the stochastic analysis combined with the set-membership filtering method, some sufficient conditions are established in the form of recursive matrix inequalities and the filter gain matrix is obtained in terms of the solution to these matrix inequalities. Finally, a simulation example is provided to show the effectiveness of the proposed filtering design scheme.