## Parameter-dependent robust $$H_\infty$$ filtering for uncertain discrete-time systems.(English)Zbl 1158.93406

Summary: This paper is concerned with the problem of parameter-dependent $$H_\infty$$ filtering for discrete-time systems with polytopic uncertainties. The uncertain parameters are supposed to reside in a polytope. Being different from previous results in the quadratic framework, the parameter-dependent Lyapunov function is used in this paper. Both full- and reduced-order filters are designed, which guarantee the asymptotic stability and a prescribed $$H_\infty$$ performance level. The filter parameters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Numerical examples are presented to illustrate the feasibility and less conservativeness of the proposed method.

### MSC:

 93E11 Filtering in stochastic control theory 93C55 Discrete-time control/observation systems

LMI toolbox
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### References:

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