Reliable control for a class of uncertain singular systems with interval time-varying delay.

*(English)*Zbl 1219.93105Summary: This paper is concerned with the reliable controller design problem for a class of singular systems with interval time-varying delay and norm-bounded uncertainties. A more practical model of actuator failures than outages is considered. First, by constructing a novel Lyapunov-Krasovskii functional combined with Finsler’s Lemma, an improved delay-range-dependent stability criterion for the nominal unforced singular time-delay system is established in terms of linear matrix inequality. Then, based on this criterion, an LMI condition for the design of a reliable state feedback controller is presented such that, for all parameter uncertainties and actuator failures, the resultant closed-loop system is regular, impulse-free and stable. Numerical examples are proposed to illustrate the effectiveness of the proposed method.

##### MSC:

93D20 | Asymptotic stability in control theory |

93C15 | Control/observation systems governed by ordinary differential equations |

93B52 | Feedback control |

93C05 | Linear systems in control theory |

34H05 | Control problems involving ordinary differential equations |

##### Keywords:

singular time-delay systems; delay-range-dependent; reliable control; actuator failure; norm-bounded uncertainty
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\textit{J. Lin} and \textit{S. Fei}, Asian J. Control 13, No. 4, 542--552 (2011; Zbl 1219.93105)

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##### References:

[1] | Hale, Introduction to Functional Differential Equations (1993) · Zbl 0787.34002 |

[2] | Xu, Robust stability sand stabilization for singular systems with state delay and parameter uncertainty, IEEE Trans. Autom. Control 47 (7) pp 1122– (2002) · Zbl 1364.93723 |

[3] | Fridman, H control of linear state-delay descriptor systems: an LMI approach, Linear Alg. Appl. 351-352 pp 271– (2002) · Zbl 1006.93021 |

[4] | Su, Delay-dependent robust control for uncertain singular time-delay systems, Asian J. Control 8 (2) pp 1– (2006) |

[5] | Zhong, Delay-dependent robust control of descriptor systems with time delay, Asian J. Control 8 (1) pp 36– (2006) |

[6] | Du, Delay-dependent robust H control for uncertain singular systems with multiple state delays, IET Control Theory Appl. 3 (6) pp 731– (2009) |

[7] | Zhu, Delay-dependent robust stability criteria for two classes of uncertain singular time-delay systems, IEEE Trans. Autom. Control 52 (5) pp 880– (2007) · Zbl 1366.93478 |

[8] | Wu, Delay-dependent robust H control for uncertain singular time-delay systems, IET Control Theory Appl. 1 (5) pp 1234– (2007) |

[9] | Xu, An improved characterization of bounded realness for singular delay systems and its applications, Int J. Robust Nonlinear Control 18 (3) pp 263– (2008) · Zbl 1284.93117 |

[10] | Wu, Passivity-based sliding mode control of uncertain singular time-delay systems, Automatica 45 (9) pp 2120– (2009) · Zbl 1175.93065 |

[11] | Wang, Absolute stability criteria for a class of nonlinear singular systems with time delay, Nonlinear Anal. Theory Methods Appl. 70 (2) pp 621– (2009) · Zbl 1168.34048 |

[12] | Jiang , Z. W. Gui Y. Xie H. Wu Delay-dependent stabilization of singular linear continuous-time systems with time-varying state and input delays 1862 1867 |

[13] | Wang , H. A. Xue R. Lu J. Wang Delay-dependent robust stability and stabilization for uncertain singular system with time-varying delay 1327 1331 |

[14] | Lu, Delay-dependant robust stability and stabilization conditions for a class of Lur’e singular time-delay systems, Asian J. Control 10 (4) pp 462– (2008) |

[15] | Li, Observer-based resilient L2-L control for singular time-delay systems, IET Control Theory Appl. 3 (10) pp 1351– (2009) |

[16] | Kim, Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays, Int. J. Control, Autom., Syst. 7 (3) pp 357– (2009) |

[17] | Gu, Further remarks on additional dynamics in various model transfor-mation of linear delay systems, IEEE Trans. Autom. Control 46 (3) pp 497– (2001) · Zbl 1056.93511 |

[18] | He, Delay-range-dependent stability for systems with time-varying delay, Automatica 43 (2) pp 371– (2007) · Zbl 1111.93073 |

[19] | Gao, A new delay system approach to network-based control, Automatica 44 (1) pp 39– (2008) · Zbl 1138.93375 |

[20] | Liang, State estimation for coupled uncertain stochastic networks with missing measurements and time-varying delays: the discrete-time case, IEEE Trans. Neural Netw. 20 (5) pp 781– (2009) |

[21] | Wang, Robust H control for a class of nonlinear discrete time-delay stochastic systems with missing measurements, Automatica 45 (3) pp 684– (2009) · Zbl 1166.93319 |

[22] | MacFarlane, Complex Variable Methods for Linear Multivariable Feedback Systems (1980) |

[23] | Yang, Reliable control of discrete-time systems with actuator failure, IEE Proc., Control Theory Appl. 147 (4) pp 428– (2000) |

[24] | Yu, An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure, Appl. Math. Comput. 162 (3) pp 1325– (2005) · Zbl 1125.93046 |

[25] | Ye, Reliable guaranteed cost control for linear state delayed systems with adaptive memory state feedback controllers, Asian J. Control 10 (6) pp 678– (2008) |

[26] | Yue, Reliable H control of uncertain descriptor systems with multiple time delays, IEE Proc., Control Theory Appl. 150 (6) pp 557– (2003) |

[27] | Dai, Singular Control Systems (1989) · Zbl 0669.93034 |

[28] | de Souza, Robust H filtering for discrete-time linear systems with uncertain time-varying parameters, IEEE Trans. Signal Process. 54 (6) pp 2110– (2006) · Zbl 1373.93337 |

[29] | Cao, Delay dependent robust H control for uncertain systems with time-varying delays, IEE Proc., Control Theory Appl. 145 (3) pp 338– (1998) |

[30] | Lam, Stability analysis for continuous systems with two additive time-varying delay components, Syst. Control Lett. 56 (1) pp 16– (2007) · Zbl 1120.93362 |

[31] | Yue, A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay, Int. J. Robust Nonlinear Control 19 (13) pp 1493– (2009) · Zbl 1298.93259 |

[32] | Zhang, A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays, Int. J. Robust Nonlinear Control 19 (17) pp 1922– (2009) · Zbl 1185.93106 |

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