##
**Improved stability criteria and controller design for linear neutral systems.**
*(English)*
Zbl 1185.93102

Summary: This paper is concerned with the problems of stability and \(H_\infty \) control of linear neutral systems. Firstly, some new simple Lyapunov-Krasovskii functionals are constructed by uniformly dividing the discrete delay interval into multiple segments, and choosing proper functionals with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functionals. Then using these new simple Lyapunov-Krasovskii functionals, some new delay-dependent stability criteria are derived. These criteria include some existing results as their special cases and are much less conservative than some existing results, which is shown through a numerical example. Secondly, a delay-dependent Bounded Real Lemma (BRL) is established. Employing the obtained BRL, some delay-dependent sufficient conditions for the existence of a delayed state feedback controller, which ensure asymptotic stability and a prescribed \(H_\infty \) performance level of the corresponding closed-loop system, are formulated in terms of a linear matrix inequality. A numerical example is also given to illustrate the effectiveness of the design method.

### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93B51 | Design techniques (robust design, computer-aided design, etc.) |

34K40 | Neutral functional-differential equations |

93D20 | Asymptotic stability in control theory |

Full Text:
DOI

### References:

[1] | Chen, J.-D.; Lien, C.-H.; Fan, K.-K.; Chou, J.-H., Criteria for asymptotic stability of a lass of neutral systems via a LMI approach, IEE Proceedings - Control Theory and Applications, 148, 442-447 (2001) |

[2] | Chen, Y.; Xue, A.; Lu, R.; Zhou, S., On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations, Nonlinear Analysis, Theory, Methods and Applications, 68, 2464-2470 (2008) · Zbl 1147.34352 |

[3] | Fridman, E., New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems, Systems and Control Letters, 43, 309-319 (2001) · Zbl 0974.93028 |

[4] | Fridman, E.; Shaked, U., A descriptor system approach to \(H_\infty\) control of linear time-delay systems, IEEE Transactions Automation Control, 47, 253-270 (2002) · Zbl 1364.93209 |

[5] | Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems (2003), Birkhäuser: Birkhäuser Boston · Zbl 1039.34067 |

[6] | Gouaisbaut, F., & Peaucelle, D. (2006a). Delay-dependent robust stability of time delay systems. In IFAC-ROCOND; Gouaisbaut, F., & Peaucelle, D. (2006a). Delay-dependent robust stability of time delay systems. In IFAC-ROCOND · Zbl 1293.93589 |

[7] | Gouaisbaut, F., & Peaucelle, D. (2006b). Delay-dependent stability analysis of linear time delay systems. In The sixth IFAC workshop on time-delay systems; Gouaisbaut, F., & Peaucelle, D. (2006b). Delay-dependent stability analysis of linear time delay systems. In The sixth IFAC workshop on time-delay systems · Zbl 1293.93589 |

[8] | Han, Q.-L.; Yu, X.; Gu, K., On computing the maximum time-delay bound for stability of linear neutral systems, IEEE Transactions Automation Control, 49, 2281-2286 (2004) · Zbl 1365.93224 |

[9] | Han, Q.-L., On stability of linear neutral systems with mixed time-delays: A discretized Lyapunov functional approach, Automatica, 41, 2171-2176 (2005) · Zbl 1100.93519 |

[10] | Han, Q.-L., A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices, International Journal of Systems Science, 36, 469-475 (2005) · Zbl 1093.34037 |

[11] | Han, Q.-L. (2008). A delay decomposition approach to stability of linear neutral systems. In Proceedings of the 17th IFAC world congress; Han, Q.-L. (2008). A delay decomposition approach to stability of linear neutral systems. In Proceedings of the 17th IFAC world congress |

[12] | He, Y.; Wu, M.; She, J. H.; Liu, G. P., Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems and Control Letters, 51, 57-65 (2004) · Zbl 1157.93467 |

[13] | Lien, C.-H.; Chen, J.-D., Discrete-delay-independent and discrete-delay-dependent criteria for a class of neutral systems, ASME Journal of Dynamic Systems, Measurement and Control, 125, 33-41 (2003) |

[14] | Ochoa, B.M., & Mondie, S. (2007). Approximations of Lyapunov-Krasovskii functionals of complete type with given cross terms in the derivative for the stability of time-delay systems. In Proceedings of the 46th IEEE CDC; Ochoa, B.M., & Mondie, S. (2007). Approximations of Lyapunov-Krasovskii functionals of complete type with given cross terms in the derivative for the stability of time-delay systems. In Proceedings of the 46th IEEE CDC |

[15] | Wang, Z.; Lam, J.; Burnham, K. J., Stability analysis and observer design for neutral delay systems, IEEE Trans. Autom. Control, 47, 478-483 (2002) · Zbl 1364.93100 |

[16] | Yue, D.; Sangchul, W., Delay dependent stability of neutral systems with time delay: LMI approach, IEE Proceedings - Control Theory and Applications, 150, 23-27 (2003) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.