Stability Analysis for Hybrid Time-Delay Systems With Double Degrees

In this article, the problem of stability is investigated for a class of hybrid time-delay systems with double degrees. The systems consist of both discrete and continuous subsystems that have homogeneity and nonzero degrees. Conditions are derived to guarantee the preasymptotic stability of the systems. The relationships of solutions are established between the systems with different sizes using homogeneous properties. Then, equivalent conditions are presented for the analysis of preasymptotic stability. Furthermore, necessary and sufficient delay-independent conditions are developed to analyze the stability of the systems. Finally, two examples are provided to illustrate the effectiveness of the proposed new stability analysis methods.