Fixed/Preassigned-Time Stability of Time-Varying Nonlinear System With Discontinuity: Application to Chua’s Circuit

This brief studies the fixed/preassigned-time stability problems for a class of time-varying discontinuous system modeled by ordinary differential equation (ODE). By using a special exponential function and developing an indefinite derivative Lyapunov function method, the novel fixed-time stability (FXTS) and preassigned-time stability (PATS) criteria are established, where the settling-time (S-T) of FXTS is estimated and the preassigned-time is given for PATS. Then the established FXTS/PATS results are applied to achieve the fixed/preassigned-time stabilization of Chua’s circuit system (CCS) by designing switching external control input.