Novel variance-constrained filtering for uncertain systems subject to randomly varying sensor delay

In this paper, the problem of robust filtering for a class of uncertain discrete-time stochastic systems under randomly varying distributed sensor delay is reconsidered. A new and efficient method for robust filter design is introduced to achieve some performance requirements, that is, the error state of filtering process is mean square bounded and the steady-state variance of the estimation error for each state is less than the individual prescribed upper bound. Different from the previous method which involves a two-step design procedure with algebraic Riccati-like inequalities and linear constraint, it is shown that this problem can be directly converted to the feasibility of some linear matrix inequalities. Furthermore, the inequality used for handling the parameter uncertainty in the previous literature is no required which reduces the conservatism of the obtained results. An example is carried out to illustrate the effectiveness of the method and the improvement over the existing result in the literature.