Adaptive robust stabilization of a class of uncertain non-linear systems with mismatched time-varying parameters

In this paper, an adaptive robust stabilization algorithm is presented for a class of non-linear systems with mismatched uncertainties. In this regard, a new controller based on the Lyapunov theory is proposed in order to overcome the problem of stabilizing non-linear time-varying systems with mismatched uncertainties. This method is such that the stability of the closed-loop system is guaranteed in the absence of the triangularity assumption. The proposed approach leads to asymptotic convergence of the states of the closed-loop system to zero for unknown but bounded uncertainties. Subsequently, this method is modified so that all the signals in the closed-loop system are uniformly ultimately bounded. Eventually, numerical simulations support the effectiveness of the given algorithm.