Zero-dynamics design and its application to the stabilization of implicit systems

We present a formula that computes the output of an R-controllable, regular, single-input linear timeinvariant implicit system in such a way that it has prescribed relative degree and zeros. The formula is inspired on different generalizations of Ackermann’s formula. A possible application is in the context of sliding-mode control of implicit systems where, as the first step, one can use the proposed formula to design a sliding surface with desired dynamic characteristics and, as the second step, apply a higher-order sliding-mode controller to enforce a sliding motion along the resulting sliding surface.