L2-Performance Analysis for Sandwich Systems with Backlash

This paper addresses the problems of performance and stability analysis for a certain class of nonlinear systems resulting from a sandwiched backlash operator in the connection of a plant and an actuator device, and subject to Lscr₂-limited time-derivative disturbance. Constructive conditions based on LMIs to ensure both the internal stability and the trajectories boundedness of the sandwich system are proposed by using some suitable Lyapunov functionals and generalized sector conditions. The associated set of all the admissible equilibrium points is precisely defined. Some extensions to the case where some parameters of the backlash nonlinearity are uncertain are also provided