Semiglobal stabilization via measurement feedback for systems in triangular form

In this paper we consider the problem of semiglobally stabilizing a wide class of uncertain nonlinear system, which is made up of a linear nominal system affected by model uncertainties or nonlinearities. Our approach is based on H∞ control tools and recovers existing results on the semiglobal stabilization via output feedback. We will prove that, if the uncertainties satisfy both a triangularity property (TS) and a linearity property (LS) with respect to some state variables, we can achieve semiglobal stabilization via measurement feedback. The resulting measurement feedback is itself 'optimal' with respect to a 'meaningful' cost functional. Our result also allows to take into account output nonlinear effects such as saturations and backlash.