Vector Control Lyapunov Function based Stabilization of Nonlinear Systems in Predefined Time

Predefined-time stability is the of dynamical systems whose solutions approach equilibrium point within a pre-decided time duration. In this technical note, we develop general results predefined-time nonlinear using vector Lyapunov functions. A comparison system, which predefined convergent, constructed, and after that original system proved differential inequalities principles. Moreover, design controllers for large-scale control functions (VCLFs). Sliding mode introduced in to mitigate matched bounded disturbances/uncertainties. Also, aggregate reduce their dimensionality order effectively apply derived on practical systems. The theoretical are implemented 2 DOF Helicopter model.