Stability analysis for time-delayed systems of retarded-type with inequitable/equitable multiple-sectional approaches

In this paper, stability analysis of time-delayed systems of retarded-type with single time delays is examined by means of inequitable and equitable multiple-sectioning of the time delays. More precisely, we introduce generalized Lyapunov functionals including sub-integrals with piecewise constant weighting matrices to deal with time delay multiple sectioning. Two stability criteria in terms of LMI are derived and proved. It is also examined under some special weighting matrices cases to reduce sufficiency redundancy via adopting sub-optimal segmentation positions or increasing segmentation number as appropriately. The suggested approach can provide us with more precise estimation information about upper bounds for allowable time delay when the time-delayed system remains asymptotically stable. Numerical examples are included to illustrate our main results.