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For a multirate sample-data system where the output sampling rate is slower than the input updating rate, we study the l 2 -l ∞ filtering problems for fast state estimation by using the lifted model. The filtering problem is handled in the framework of linear matrix inequalities (LMIs) with a nonconvex constraint, which is numerically solved by the product reduction algorithm. Finally, the effectiveness of the proposed method is illustrated and verified by simulation examples.

This paper considers the discrete‐time ${\cal H}_2$ output tracking control of wireless networked control systems (NCSs) where the time delays are modeled as Markov chains. Output tracking control can find many applications in industry. In order to reduce the conservativeness and achieve better performance, the designed state feedback controller is dependent on available sensor‐to‐controller and controller‐to‐actuator delays. Then, the formulated closed‐loop system is a special jump linear system governed by interdependent parameters of Markov chains and the condition for stochastic stability is proposed. By generalization of the ${\cal H}_2$ norm definition, new relation of the ${\cal H}_2$ norm for the special system is derived in terms of state space form. The condition of a set of linear matrix inequalities (LMIs) with nonconvex constraints is given to solve the ${\cal H}_2$ output tracking control problem. Simulation examples are provided to illustrate the effectiveness of the method. Copyright © 2009 John Wiley & Sons, Ltd.

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