Global robustness of nonlinear systems to state measurement disturbances

We consider nonlinear control systems for which an estimate xˆ of the system state x is available for feedback. We assume xˆ=x+d_m, where d_m(t) is an unknown locally bounded state measurement disturbance. We present conditions under which we can design a smooth feedback law u=μ(xˆ) which renders the mapping from d_m to x globally input/output stable. For any initial condition, such a feedback law will guarantee that no finite escape times occur, that bounded disturbances d_m produce bounded signals, and that x→0 when d_m→0. We show that the class of systems for which such feedback laws exist include systems in strict feedback form. One important application is in the output feedback stabilization problem, where the disturbance d_m comes from a separately designed observer