Delay-Hybrid-Dependent Stability for Systems With Large Delays

This paper investigates a problem of stability analysis for a class of nonlinear systems with a time-varying delay taking both large and small values in an alternating manner. This problem is a delay-dependent stability analysis one but it shares some features with delay-independent ones. Hence, traditional stability analysis techniques for systems with delay are not applicable. By building upon our previous works, we first introduce the concept of delay-hybrid-dependent stability, which characterizes the delays described above. The considered system is first represented as a system with a switched delay. Then by using switching techniques and Lyapunov-Krasovskii functionals (LKFs), a new stability criterion is developed. Next, in the linear context, it is shown how the needed LKFs can be constructed by developing an original design of LKFs.