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**Robust stability criteria for uncertain neutral systems with interval time-varying delay.**
*(English)*
Zbl 1222.93174

Summary: We consider the problem of robust stability of a class of linear uncertain neutral systems with interval time-varying delay under (i) nonlinear perturbations in state, and (ii) time-varying parametric uncertainties using the Lyapunov-Krasovskii approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of Linear Matrix Inequalities (LMI) to compute the maximum allowable bound for the delay-range within which the uncertain neutral system under consideration remains asymptotically stable. The reduction in conservatism of the proposed stability criterion over recently reported results is attributed to the fact that time-derivative of the LK functional is bounded tightly without neglecting any useful terms using a minimal number of slack matrix variables. The analysis, subsequently, yields a stability condition in convex LMI framework, that can be solved non-conservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.

### MSC:

93D09 | Robust stability |

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

93C05 | Linear systems in control theory |

34K40 | Neutral functional-differential equations |

### Keywords:

neutral system; robust stability; interval time-varying delay; delay-range-dependent stability; linear matrix inequality
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\textit{K. Ramakrishnan} and \textit{G. Ray}, J. Optim. Theory Appl. 149, No. 2, 366--384 (2011; Zbl 1222.93174)

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