Stability analysis for linear systems with asymmetric input backlash and dead-zone through LMI conditions

This paper deals with the stability analysis of the interconnection between a linear system and a nonlinear operator. This operator is the combination between an asymmetric backlash and a dead-zone. It is a memory-based operator which is only piecewise differentiable. To handle such a nonlinearity, which is more complex than the standard ones, we aim to capture the closed-loop trajectories in some suitable regions of the state space. Uniform Ultimate Boundednes (UUB) property is addressed, using the intrinsic behavior of the operator and a Lyapunov-based approach. Sufficient conditions are provided in terms of Linear Matrix Inequalities (LMIs). A numerical illustration is presented to assess our contribution.