Fixed-time and finite-time stability of switched time-delay systems

This paper investigates fixed-time and finite-time stability of switched nonlinear time-varying time-delay systems. It is shown that by assuming these kinds of stability for each subsystem in the family, the similar properties can be ensured for the whole system under commutation with a sufficiently big (average) dwell time. The estimates on admissible dwell-time values are derived. Compared with existing results, the novelties of the obained results lie in that: (i) A class of Lyapunov-Krasovskii functionals with inde nite derivative is constructed for switched nonlinear time-delay systems, (ii) Average dwell time switching laws are designed for the fixed-time and finite-time stability of the systems, and (iii) The presented approach has potential applications in fixed-time and finite-time stability of other hybrid systems. The efficacy of the obtained results is illustrated by academic examples.

Automated summary

This paper investigates the fixed-time and finite-time stability of switched nonlinear time-varying time-delay systems, constructing Lyapunov-Krasovskii functionals with indefinite derivative and designing average dwell time switching laws. The results obtained show potential applications in stability analysis of other hybrid systems.