Further results on π-trajectories of Lipschitz stabilizers

The definitions of π-trajectories of nonnecessary continuous feedback and of s-stability were introduced by Clarke et al. (1996). In this work we prove that a Lipschitz stabilizer is an s-stabilizer, and we give a sufficient condition for the convergence of the π-trajectories of this class of stabilizers to the origin. When the digital implementation of Lipschitz stabilizers is carried out by sampling and zero-order hold (SZH) with nonconstant sampling rate the trajectories of the resulting system are π-trajectories. In consequence these results are an extension of the authors´ previous results (1997) related to the digital implementation of feedback stabilization laws of nonlinear continuous time control systems