Stabilization by Output Feedback of Multivariable Invertible Nonlinear Systems

In this paper, the problem of global stabilization of a rather general class of MIMO nonlinear systems is addressed. The systems considered in the paper are invertible, have a trivial zero dynamics and possess a “normal form” in which certain multipliers are functions of the state vector of a special kind. While special structural dependence of such multipliers on the components state vector has been exploited before in the context of achieving stabilization (via full-state feedback, though), the novelty in the approach of this paper is that a peculiar structure is identified which happens to be intimately related to the property of uniform complete observability (thus making the design of observers possible) and to the property of uniform invertibility, relations never established before in the literature. As a result, for this class of MIMO nonlinear systems, a dynamic output feedback law can be designed, yielding semiglobal (and even global, under appropriate assumptions) asymptotic stability.