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**A less conservative method for designing \(H_{\infty}\) filters for linear time-delay systems.**
*(English)*
Zbl 1169.93418

Summary: This paper focuses on \(H_\infty\) filtering for linear time-delay systems. A new Lyapunov-Krasovskii Functional (LKF) is constructed by uniformly dividing the delay interval into two subintervals, and choosing different Lyapunov matrices on each subinterval. Based on this new LKF, a less conservative delay-dependent Bounded Real Lemma (BRL) is established to ensure that the resulting filtering error system is asymptotically stable with a prescribed \(H_\infty\) performance. Then, this new BRL is equivalently converted into a set of linear matrix inequalities, which guarantee the existence of a suitable \(H_\infty\) filter. Compared with some existing filtering results, some imposed constraints on the Lyapunov matrices are removed through derivation of the sufficient condition for the existence of the filter. Numerical examples show that the results obtained in this paper significantly improve the \(H_\infty\) performance of the filtering error system over some existing results in the literature.

### MSC:

93E11 | Filtering in stochastic control theory |

93E10 | Estimation and detection in stochastic control theory |

93D30 | Lyapunov and storage functions |

93C05 | Linear systems in control theory |

### Keywords:

linear systems; \(H_{\infty}\) filtering; bounded real Lemma (BRL); time-delay; Lyapunov-Krasovskii functional (LKF)
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\textit{X.-M. Zhang} and \textit{Q.-L. Han}, Int. J. Robust Nonlinear Control 19, No. 12, 1376--1396 (2009; Zbl 1169.93418)

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