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Robust $H_\infty$ filtering for switched linear discrete-time systems with polytopic uncertainties. (English) Zbl 1127.93324
Summary: The problem of robust $H_\infty$ filtering for switched linear discrete-time systems with polytopic uncertainties is investigated. Based on the mode-switching idea and parameter-dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed $H_\infty$ performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal $H_\infty$ noise-attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques.

93B35Sensitivity (robustness) of control systems
93E11Filtering in stochastic control
93C55Discrete-time control systems
93C41Control problems with incomplete information
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