## Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions.(English)Zbl 1022.93048

This paper regards the robust filtering problem for linear time-invariant discrete-time systems using parameters dependent Lyapunov functions, when convex polytopic uncertainty is present in the dynamic, input, or output matrices. It bases on a new robust stability condition presenting a separation between the Lyapunov matrix and the matrices of the dynamic model. It is shown how to use such an approach to determine high performance $$H_2$$ robust filters. Numerical examples illustrate the theoretical results.

### MSC:

 93E11 Filtering in stochastic control theory 93C55 Discrete-time control/observation systems 93C05 Linear systems in control theory 93E15 Stochastic stability in control theory 93D30 Lyapunov and storage functions
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