Computer algebra design of continuous stabilizers for singular triangular systems

The goal of this paper is three fold. Firstly, an algorithm is developed which allows to design continuous stabilizers for triangular systems. The algorithm is based on new theoretical results on asymptotic feedback stabilization of triangular systems. These results provide an explicit method for the design of the stabilizing feedback and demonstrate the asymptotic stability of the closed loop system for a certain subclass of triangular systems. This subclass includes some of the so-called singular triangular systems, i.e. those having uncontrollable or even nonstabilizable linear approximation. Therefore, unavoidably the proposed feedback is continuous only. Secondly, employing the above algorithm, a bundle of computer algebra programs is implemented, which allows to automatically compute a continuous stabilizer for any given triangular system. Several particular examples are studied to test all these procedures, including the case study of an underactuated weakly coupled mechanical system. Finally, some outlooks are given about the stability proof for the case of general singular triangular systems. Even though the proof is not complete at this stage, some very interesting properties of the closed loop system are put forward, including some properties which are of interest even from dynamical systems´ point of view