Further Results on Fast Finite-Time Stability Criteria and Its Application in Circuit System

This brief presents a novel approach for fast finite-time adaptive control of uncertain nonlinear systems. First, practical fast finite-time stability criteria are established for both deterministic nonlinear systems and stochastic nonlinear systems with rigorous proofs, taking the case of
$\beta =1$
in literature as a special case. A useful corollary is also explored to address a wider range of issues. These new criteria not only apply to generalized uncertain nonlinear systems with certain and uncertain components but also provide a new perspective to reduce convergence time while handling positive error
$\Delta $
. Additionally, simulation results for the proposed criteria applied to a circuit system are provided. The results show that the proposed approach allows for fast convergence time, and the convergence time can be adjusted by the initial value.