Relaxing the conditions for parameter estimation-based observers of nonlinear systems via signal injection

Parameter estimation-based observers are a new kind of state reconstruction methods where the state observation task is translated into an on-line parameter estimation problem. A key step for its application is the transformation of the system dynamics into a particular cascade form, which involves the solution of a partial differential equation that, moreover, should satisfy some injective requirement. In this note we use a recently proposed technique of signal injection to generate new outputs and simplify these tasks. In this way, we make this observer applicable to a wider class of nonlinear systems-even with indistinguishable states. The application of the proposed approach is illustrated with the design of a novel sensorless controller for magnetic levitation systems.