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

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

Automated summary

This technical note investigates the predefined-time stability of nonlinear systems using vector Lyapunov functions. A predefined-time convergent vector comparison system is constructed, and the stability of the original dynamical system is proved using differential inequalities and comparison principles. Predefined-time controllers for large-scale systems are designed using vector control Lyapunov functions, with the introduction of sliding-mode control to mitigate matched bounded disturbances/uncertainties. Comparison systems are aggregated to reduce dimensionality for practical system applications.