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Robust \(l_2\)-\(l_\infty\) control for uncertain discrete-time switched systems with delays. (English) Zbl 1112.93046

Summary: This paper is concerned with the problem of robust \(l_2\)-\(l_\infty\) control for uncertain discrete-time switched systems with time delay in the state. The uncertainty is assumed to be of structured linear fractional form which includes the norm-bounded uncertainty as a special case. The control design approach is facilitated by introducing some additional instrumental matrix variables. The additional matrix variables decouple the Lyapunov and system matrices, which make the control design feasible. The proposed approach leads to less conservativeness of previous design methods, and the results also generalize earlier works for a more general parametric uncertainty structure. A numerical example is also given to demonstrate the effectiveness and the potential of the proposed techniques.

MSC:

93C55 Discrete-time control/observation systems
93B35 Sensitivity (robustness)
93C41 Control/observation systems with incomplete information
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