## 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.

### MSC:

 9.3e+12 Filtering in stochastic control theory 9.3e+16 Stochastic stability in control theory
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### References:

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