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**A delay-dependent bounded real lemma for singular LPV systems with time-variant delay.**
*(English)*
Zbl 1273.93088

Int. J. Robust Nonlinear Control 22, No. 5, 559-574 (2012); corrigendum ibid. 23, No. 5, 590 (2013).

Summary: This paper is concerned with establishing a delay-dependent Bounded Real Lemma (BRL) for singular Linear Parameter-Varying (LPV) systems with time-variant delay. In terms of linear matrix inequality, a delay-dependent BRL is presented to ensure singular time-delay LPV systems to be admissible and satisfy a prescribed \(H_{\infty }\) performance level. The BRL is obtained based on the construction of a parameter-dependent Lyapunov-Krasovskii functional. The effectiveness of the proposed approach is shown by several numerical examples.

### MSC:

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

93C05 | Linear systems in control theory |

93B36 | \(H^\infty\)-control |

93D99 | Stability of control systems |

### Keywords:

singular linear parameter-varying (LPV) systems; time-variant delay; bounded real lemma; stability
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\textit{F. Li} and \textit{X. Zhang}, Int. J. Robust Nonlinear Control 22, No. 5, 559--574 (2012; Zbl 1273.93088)

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