Adaptive Dynamic Surface Control: Stability Analysis Based on LMI

In this paper, quadratic stability of adaptive dynamic surface control for a class of nonlinear systems in strict-feedback form is analyzed in the framework of linear matrix inequality. While the existence of controller gains and filter time constants for semi-global stability was theoretically proved in the literature, it is not sufficient to describe how a set-point value and parameter update laws affect stability and parameter convergence. Thus, it is necessary to provide a systematic analysis method to guarantee both stability and parameter convergence. By deriving the augmented closed-loop error dynamics in linear differential inclusion form, a sufficient condition of the controller gains for stability and parameter convergence is derived in the form of linear matrix inequality. Finally, the quadratic Lyapunov function for its quadratic stability is computed numerically via convex optimization.