Finite-time semi-global stabilisation of polynomial growth nonlinear systems by linear time-varying feedback

The paper studied the finite-time semi-global stabilisation problems for a class of nonlinear systems with a novel polynomial growth condition. By using some key properties of a class of parametric Lyapunov equations and constructing time-varying Lyapunov-like functions, two time-varying high-gain controllers, where scalar time-varying functions are generated by differential equations, are designed. Both state feedback and observer-based output feedback are considered. It is shown that the proposed methods can achieve finite-time semi-global stabilisation for closed-loop systems and the controls are bound. Two numerical examples verify the effectiveness of the established results.