Semiglobal stabilization via measurement feedback for systems in triangular form

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 prove that if the uncertainties satisfy both a triangularity property and a linearity property 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