Direct adaptive control for nonlinear uncertain systems with bounded energy L2 disturbances

A direct adaptive nonlinear control framework for multivariable nonlinear uncertain systems with exogenous L₂ disturbances is developed. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system, i.e., the asymptotic stability with respect to part of the closed-loop system states associated with the plant as well as a nonexpansivity constraint on the closed-loop input-output map. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach