Fuzzy control of second order vectorial systems: L2 stability

The L₂ stability criterion is defined only when we have squared control systems. However, it is very common that Fuzzy Control Systems-FCS-(plants + fuzzy controllers) have MISO Fuzzy Controllers regulating SISO plants. This document proposes a way that can study the L₂ stability in FCS when the Fuzzy Control is MISO and the plant is SISO or MIMO by means of the sliding control and passivity theory. Practically, there is no references about it and this paper tries to give an apportation in this sense. The class of plants to control belongs to the wide class of systems known as Second Order Vectorial Systems (SOVS) or Euler - Lagrange Systems (ELS). In this sense, both the non linear and the linear case are aboarded.