On design of reduced-order H∞ filters for discrete-time systems from incomplete measurements

In networked control systems, when data are transmitted over wireless channels, measurements of the transmitted data are often incomplete due to transmission errors and/or packet losses. The problem of designing reduced-order H_∞ filters for discrete-time systems from incomplete measurements is investigated in this paper. A Bernoulli distributed white sequence is adopted as a model for the normal operating condition of packet delivery and transmission failure. The reduced-order filter to be designed from incomplete measurements is required to to ensure the mean-square stability of the filtering error system and to guarantee a prescribed H_∞ filtering performance level. It is shown that such a desired reduced-order H_∞ filter can be constructed under a sufficient condition expressed in terms of two linear matrix inequalities (LMIs) subject to a rank constraint.