Sliding Mode Control for Two-Time Scale Systems: Stability Issues
Résumé
The paper presents some results on global exponential stability of linear time invariant systems with different time scales. The full system is decomposed in two reduced ones by means of singular perturbations and a smooth approximation of a Variable Structure Control is synthesized for each of them using Reaching Law approach. The global closed loop stability is then proved for the whole system using Lyapunov methods and a particular state space decomposition. Moreover a literal form for \epsilon* (a parameter which measures the minimum separation between time scales) is derived.