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Optimal ${ℋ}_{2}$ filtering with random sensor delay, multiple packet dropout and uncertain observations. (English) Zbl 1140.93486
Summary: This paper studies the problem of optimal filtering of discrete-time systems with random sensor delay, multiple packet dropout and uncertain observation. The random sensor delay, multiple packet dropout or uncertainty in observation is transformed to a stochastic parameter in the system representation. A new formulation enables us to design an optimal filter for a system with multiple packet dropout in sensor data. Based on a stochastic definition of the ${ℋ}_{2}$-norm of a system with a stochastic parameter, new relations for a stochastic ${ℋ}_{2}$-norm are derived. The stochastic ${ℋ}_{2}$-norm of the estimation error is used as a criterion for the filter design. The relations derived for the new norm definition are used to obtain a set of linear matrix inequalities (LMIs) to solve the filter design problems. Simulation examples show the effectiveness of the proposed method.
##### MSC:
 9.3e+12 Filtering in stochastic control 9.3e+16 Stochastic stability