Simplified adaptive control via improved robust positive real conditions

Simple adaptive controllers are derived by applying a new method for achieving robust strictly positive real plants via state-feedback. A constant statefeedback gain is derived that guarantees the strictly positive realness of the closed-loop in presence of polytopic type parameter uncertainties in the model that describes the plant. This is achieved by assigning different Lyapunov functions to each of the vertices of the uncertainty polytope. The obtained feedback gain is used to derive a robust simplified adaptive control of systems with polytopic uncertainties.