Stability analysis of linear systems with time-varying delay via intermediate polynomial-based functions.

This note is devoted to stability analysis for linear system with time-varying delay. By advisably introducing slack matrices, novel fractional order intermediate polynomial-based functions (IPFs) are proposed. Then, the stability condition is derived for the time delay system. From configuration on fractional order polynomials, the relationships among system states are taken into account and consolidated via slack variables, and the characteristics for integral inequality are synthetically considered, while avoiding higher order time delays. More remarkably, adjusting tunable parameters also contributes to reduction of conservatism. The comparisons of computational complexity and stability region on a well known numerical example are provided to validate the advantages of the resulting stability criterion.