##
**New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems.**
*(English)*
Zbl 0974.93028

Summary: A new (descriptor) model transformation and a corresponding Lyapunov-Krasovskii functional are introduced for stability analysis of systems with delays. Delay-dependent/delay-independent stability criteria are derived for linear retarded and neutral type systems with discrete and distributed delays. Conditions are given in terms of linear matrix inequalities and for the first time refer to neutral systems with discrete and distributed delays. The proposed criteria are less conservative than other existing criteria (for retarded type systems and neutral systems with discrete delays) since they are based on an equivalent model transformation and since they require bounds for fewer terms. Examples are given that illustrate advantages of our approach.

### MSC:

93C23 | Control/observation systems governed by functional-differential equations |

93D20 | Asymptotic stability in control theory |

93B17 | Transformations |

15A39 | Linear inequalities of matrices |

### Keywords:

time-delay systems; stability; linear matrix inequalities; delay-dependent/delay-independent criteria; transformation; neutral systems; distributed delays; discrete delays
PDF
BibTeX
XML
Cite

\textit{E. Fridman}, Syst. Control Lett. 43, No. 4, 309--319 (2001; Zbl 0974.93028)

Full Text:
DOI

### References:

[1] | Charitonov, V.; Melchor-Aguilar, D., On delay-dependent stability conditions, Systems control lett., 40, 71-76, (2000) · Zbl 0977.93072 |

[2] | L. El’sgol’ts, S. Norkin, Introduction to the Theory and Applications of Differential Equations with Deviating Arguments, Mathematics in Science and Engineering, Vol. 105, Academic Press, New York, 1973. |

[3] | E. Fridman, Effects of small delays on stability of singularly perturbed systems, Automatica, submitted for publication. · Zbl 1014.93025 |

[4] | Hale, J.; Lunel, S., Introduction to functional differential equations, (1993), Springer New York · Zbl 0787.34002 |

[5] | Hale, J.; Lunel, S., Effects of small delays on stability and control, rapportnr. WS-528, (1999), Vrije University Amsterdam |

[6] | Kolmanovskii, V.; Niculescu, S.-I.; Richard, J.P., On the liapunov – krasovskii functionals for stability analysis of linear delay systems, Internat. J. control, 72, 374-384, (1999) · Zbl 0952.34057 |

[7] | Kolmanovskii, V.; Richard, J-P., Stability of some linear systems with delays, IEEE trans. automat. control, 44, 984-989, (1999) · Zbl 0964.34065 |

[8] | Li, X.; de Souza, C., Criteria for robust stability and stabilization of uncertain linear systems with state delay, Automatica, 33, 1657-1662, (1997) |

[9] | Lien, C.-H.; Yu, K.-W; Hsieh, J.-G., Stability conditions for a class of neutral systems with multiple time delays, J. math. anal. appl., 245, 20-27, (2000) · Zbl 0973.34066 |

[10] | Logemann, H.; Townley, S., The effect of small delays in the feedback loop on the stability of the neutral systems, Systems control lett., 27, 267-274, (1996) · Zbl 0866.93089 |

[11] | Mahmoud, M., Robust control and filtering for time-delay systems, (2000), Marcel Dekker New York |

[12] | M. Malek-Zavarei, M. Jamshidi, Time-Delay Systems, Analysis, Optimization and Applications, Systems and Control Series, Vol. 9, North-Holland, Amsterdam, 1987. · Zbl 0658.93001 |

[13] | Niculescu, S.-I., Further remarks on delay-dependent stability of linear neutral systems, proc. of MTNS 2000, (2000), Perpignan France |

[14] | Takaba, K.; Morihira, N.; Katayama, T., A generalized Lyapunov theorem for descriptor system, Systems control lett., 24, 49-51, (1995) · Zbl 0883.93035 |

[15] | Verriest, E.; Niculescu, S.-I., Delay-independent stability of linear neutral systems: a Riccati equation approach, (), 92-100 · Zbl 0923.93049 |

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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.