Constructive dynamic output feedback stabilization of a class of nonlinear systems

The aim of the paper is the output feedback stabilization of a class of single-input single-output (SISO) nonlinear systems. We deal with a class of systems, so-called triangular form systems, that may have unobservable and unstabilizable approximate linearization about the origin. This kind of systems, referred to as singular triangular forms, may neither be stabilized by a smooth state feedback nor smoothly detectable. However, under certain simple conditions, it is known to be stabilizable by a static state feedback. A solution to continuous dynamic output feedback stabilization is proposed. This is based on the construction of the continuous observer and nonlinear analogue of the well known separation principle. The resulting observer may be computed and tuned in a straightforward constructive way. Numerical simulation of selected examples are performed to underline the applicability of the presented approach and to illustrate good convergence of both observer and controller system.