Continuous feedback practical output regulation for a class of nonlinear systems having nonstabilizable linearisation

The problem of continuous static state feedback practical output regulation of a class of SISO nonlinear systems is considered. The aim is to construct a family of continuous static feedbacks solving practical output regulation for a class of nonlinear systems having uncontrollable and possibly nonstabilizable linear approximation. Due to that last property, smooth asymptotic output regulation may not be available, i.e. the error is not asymptotically decaying to zero and the smooth character of feedbacks can not be guaranteed. The studied class consists of SISO systems being in the local bijective triangular form that generalizes the regular (i.e. feedback linearizable) triangular forms. Computer simulations are also used to show practical applicability of the suggested approach, including the case study of an underactuated unstable two degrees of freedom mechanical system.