Stabilization of uncertain time-varying nonlinear systems with time delay based on feedback linearization

Abstract

Generally, nonlinear systems have uncertainties and a time delay. Sometimes, uncertainties and a time delay have an effect on stability of nonlinear systems. Additionally, dynamics of systems are time-varying. Therefore, our objective is to stabilize time-varying nonlinear systems to compensate uncertainties and a time delay. Firstly, we compensate the uncertainties of the system without a time delay. Before designing controllers, we use feedback linearization method to transform the system. When the bounds of the uncertainties are known, we design the controller to compensate the uncertainties based on Lyapunov redesign technique. When the bounds of the uncertainties are not known, we design the controller to estimate the bounds of the uncertainties and compensate them by using an adaptive law. The results are extended to time-varying case by using time-varying diffeomorphism. When there is a time delay at the input, we transform the system into the delay-free system before designing controllers. When the bounds of the uncertainties are known, we design the controller to compensate the uncertainties based on Lyapunov redesign technique. When the bounds of the uncertainties are not known, we design the controller to estimate the bounds of the uncertainties and compensate them by using an adaptive law. The results are extended to time-varying case by using time-varying diffeomorphism. We prove our controllers guarantee the asymptotical stability of the systems. Our results are verified by simulation and compared with other results.