Optimal \(\mathcal H_2\) 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 \(\mathcal H_{2}\)-norm of a system with a stochastic parameter, new relations for a stochastic \(\mathcal H_{2}\)-norm are derived. The stochastic \(\mathcal H_{2}\)-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.


93E11 Filtering in stochastic control theory
93E15 Stochastic stability in control theory
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