Robust H_∞ cost guaranteed integral sliding mode control for the synchronization problem of nonlinear tele-operation system with variable time-delay

This paper is devoted to the synchronization problem of tele-operation systems with time-varying delay, disturbances, and uncertainty. Delay-dependent sufficient conditions for the existence of integral sliding surfaces are given in the form of Linear Matrix Inequalities (LMIs). This guarantees the global stability of the tele-operation system with known upper bounds of the time-varying delays. Unlike previous work, in this paper, the controller gains are designed but not chosen, which increases the degree of freedom of the design. Moreover, Wirtinger based integral inequality and reciprocally convex combination techniques used in the constructed Lypunove-Krasoviskii Functional (LKF) are deemed to give less conservative stability condition for the system. Furthermore, to relax the analysis from any assumptions regarding the dynamics of the environment and human operator forces, H_∞ design method is used to involve the dynamics of these forces and ensure the stability of the system against these admissible forces in the H_∞ sense. This design scheme combines the strong robustness of the sliding mode control with the H_∞ design method for tele-operation systems which is coupled using state feedback controllers and inherit variable time-delays in their communication channels. Simulation examples are given to show the effectiveness of the proposed method.