A new approach to the stabilization of nonlinear systems via partial measurement feedback: the adding one measurement tool

We present a measurement feedback framework for the semiglobal stabilization of nonlinear systems which have not necessarily the uniform complete observability property in the sense of [11]. Rather, this class of systems has the robust detectability property from the measurements in the sense of [1]. A systematic design method is presented for the construction of measurement feedback controllers. A new basic ingredient is the “adding one measurement” tool, a natural counterpart of the “adding one integrator” well–known technique. While the second has been conceived for state feedback stabilization, the first has a natural role in the measurement feedback stabilization. Combining the “adding one integrator” and the “adding one measurement” techniques we get a systematic step– by–step method for measurement feedback stabilization, which leads to a number of new results on semiglobal measurement feedback stabilization