Robust estimation and control using command-to-state mapping

In this paper, the concept of command-to-state/output mapping is introduced for robust estimation under output feedback. Specifically, robust estimation is achieved if a command-to-state mapping of the plant converges to that of an uncertainty-free observer. It is shown using the Lyapunov direct method that, for a command-to-state mapping to be convergent, the Jacobian system corresponding to the observer (not the observer itself) should meet certain stability conditions. These conditions are in terms of algebraic Lyapunov equations, and they can be used to synthesize nonlinear observers in a similar fashion as the design of a stabilizing state-feedback control. The proposed method does not impose any structural condition and therefore it is both constructive and general.