Nonregular feedback linearization: a nonsmooth approach

solvable by means of a simple hybrid control law, i.e., it is possible to achieve global exponential stability of the zero equilibrium in the presence of (small) perturbations vanishing at the origin. The control law retains the basic properties of the discontinuous control laws proposed in [1], namely exponential convergence rate and lack of oscillatory behavior. The results presented in this note are based on the general theory developed in [15]. In this respect, the main contribution of this work is to show that, for a large class of nonholonomic systems, a robustly stabilizing control law can be explicitly designed, and it is possible to obtain explicit bounds on the admissible perturbations. REFERENCES [1] A. Astolfi, " Discontinuous control of nonholonomic systems, " Syst. Lyapunov functions and other analysis tools for switched and hybrid systems, " IEEE Trans. Logic-based switching control of a nonholonomic system with parametric modeling uncertainty , " Syst. Robust stabilization of driftless systems with hybrid open-loop/feedback control, " presented at the Amer. Abstract—In this note, we address the problem of exact linearization via nonsmooth nonregular feedback. A criterion of nonregular static state feedback linearizability is presented for a class of nonlinear affine systems with two control inputs, and its application to nonholonomic systems is briefly discussed.