Predefined-Time Robust Control of Nonlinear Delay Systems via Different Power Hamiltonian Functions

The study examines the
$H_{\infty}$
control problem of nonlinear time-delay systems (NTDSs) at a predetermined period. We design suitable Lyapunov functions and Hamiltonian functions that have various powers to apply to Hamiltonian systems involving outside disturbances and delay phenomena. Next, in order to guarantee that the NTDS stabilizes within one predeter-mined period and possess greater resistance against disturbances, a predefined-time
$H_{\infty}$
control strategy is introduced. Finally, a case serves to confirm the correctness of our findings.