## Improved robust $$H_{2}$$ and $$H_{\infty}$$ filtering for uncertain discrete-time systems.(English)Zbl 1050.93072

Summary: This paper is concerned with the robust $$H_2$$ and $$H_\infty$$ filtering problems for linear discrete-time systems with polytopic parameter uncertainty. We aim to derive a less-conservative design than existing linear matrix inequality (LMI) based sufficient conditions. It is shown that a more efficient evaluation of robust $$H_2$$ or $$H_\infty$$ performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations. When applying this new matrix inequality condition to the robust filter design, these parameters provide extra degrees of freedom in optimizing the guaranteed $$H_2$$ or $$H_\infty$$ performance and lead to a less-conservative design.

### MSC:

 93E11 Filtering in stochastic control theory 93C55 Discrete-time control/observation systems 15A39 Linear inequalities of matrices

### Software:

LMI toolbox; Optimization Toolbox
Full Text:

### References:

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