Stabilization for A Class of Second-order Nonlinear Time-Delay Systems with Input Unmodeled Dynamics by Using Dynamic Gain

The work, whose purpose lies in tackling the stabilizing control problem for a class of nonlinear systems possessing of uncertain time delays and input unmodeled dynamics, is presented in this article. Some crucial tools, that is, M-filters and dynamic gains, are applied in this work to handle uncertain time-varying delays and input unmodeled dynamics. Moreover, a stabilizer is capable to be exported by following the framework of backstepping. A Lyapunov-Krasovskii functional (LKF) with its proper structure can verify the asymptotically practically stable of the controlled system in presence of uncertain time delays when such system is acted by the established stabilizer. In addition, all signals in the formulating closed-loop system possess the property of semi-globally uniformly ultimately bounded (SGUUB). Lastly, a example, whose simulated plants are respectively numerical and engineering controlled systems, are exhibited in this article.