Neural network based observer and adaptive control design for a class of singularly perturbed nonlinear systems

This paper addresses the neural network (NN) based observer and adaptive control design for a class of singularly perturbed nonlinear (SPN) systems. Based on the Lyapunov stability theorem and the tool of linear matrix inequality (LMI), we solve observer and the controller gain matrix and a common positive-definite matrix and then a sufficient condition is derived to stabilize the SPN systems. The allowable perturbation bound ε* can be determined via some algebra inequalities, such that the proposed neural network based observer and the adaptive control will stabilize the SPN systems for all ε ϵ (0, ε*). A practical system is given to illustrate the validity of the proposed scheme.