Decentralized Variable Structure Control for Large-Scale Systems with Mismatched Time-Delay Interconnection Terms and Time-Varying Uncertainties

In this paper, a new decentralized variable structure control scheme is proposed for a class of large-scale time-delayed systems with mismatched uncertainties. To overcome the defect that neither time-delay interconnection terms nor uncertainties satisfy the conventional matching conditions, the coefficient matrix of the switching function can be designed to satisfy a new matching condition, meanwhile, satisfy the prerequisite for a given matrix related to time-delay interconnection terms to be a row diagonally predominant matrix, so that the complete invariance and the global asymptotically stable of the composite sliding mode are guaranteed. Then a simple local decentralized variable structure controller is designed based on the Lyapunov stability theorem and rational hypothesis. The effectiveness of the proposed decentralized variable structure controllers is illustrated through an numerical example.