Control Design for Linear Systems With Asymmetric Input Backlash and Dead-Zone Through LMI Conditions

The interconnection between a linear time invariant system and a nonlinear operator gathering an asymmetric backlash and an asymmetric dead-zone is studied, which are relevant in mechanics and hydraulics. This letter aims to design a controller as a static linear state feedback to ensure Uniform Ultimately Bounded (UUB) property for the closed-loop system. A UUB-Lyapunov-based approach is used to provide sufficient conditions as Linear Matrix Inequalities (LMIs) for this control design and a resulting optimization problem is offered to minimize the UUB set. A numerical illustration presents the efficiency of our contribution and related discussions.