\(l_{2}-l_{\infty }\) filter design for discrete-time singular Markovian jump systems with time-varying delays. (English) Zbl 1243.93116
Summary: The problem of \(l_{2}-l_{\infty }\) filter design for discrete-time singular systems with Markovian jump and time-varying delays is investigated in this paper. By using the delay partitioning technique, a delay-dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed \(l_{2}-l_{\infty }\) performance index. Based on the derived condition, the full-order and reduced-order filters with mode-independent characterization are designed in a unified framework. The corresponding filter parameters can be obtained by solving a set of linear matrix inequalities. The reported results not only depend upon the delay, but also depend upon the partitioning, which aims at reducing the conservatism. Two numerical examples are provided to illustrate the effectiveness of the proposed methods.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 60J75 | Jump processes (MSC2010) |
| 93C55 | Discrete-time control/observation systems |
| 93C05 | Linear systems in control theory |
Keywords:
singular systems; Markovian jump systems; delay-dependent; \(l_{2}-l_{\infty }\) filtering; linear matrix inequalityReferences:
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