A New Adaptive Second Order Sliding Mode Control Design for Complex Interconnected Systems

Abstract

In this paper, a new adaptive second order sliding mode control approach is extended to a class of complex interconnected systems with mismatched interconnections and unknown disturbances. The novel contribution of this paper is to remove two common limitations hindering the application of the sliding-mode control to complex interconnected systems: 1) the exogenous disturbances must be bounded by a known function of the outputs or by a known function of the state; 2) the control input is affected by chattering problems. First, based on a new adaptive law, a continuous decentralized adaptive sliding mode controller is designed to ensure the reachability of the system states without chattering problems by using output variables only. Second, existence conditions of linear sliding surfaces are derived to guarantee the asymptotic stability in terms of constrained linear matrix inequalities. Final, numerical examples are provided to verify the effectiveness of the proposed approach.