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A Novel Interpretation of the Invariance Condition of Mismatched Uncertain Large-Scale Systems

Viet Anh Duong and Yao-Wen Tsai*
International Journal of Control, Automation, and Systems, vol. 15, no. 4, pp.1577-1591, 2017

Abstract : "This paper presents a novel interpretation of the invariance condition of mismatched uncertain largescale systems in which uncertainties and interconnections do not satisfy the conventional invariance condition. A new sliding mode that consists of two sets of switching surfaces is proposed. In every subsystem, uncertainties and interconnections are all separated into matched and mismatched components to reduce the conservatism. As a result, new invariance conditions are derived such that each subsystem in the new sliding mode is completely invariant to both uncertainties and interconnections. We also show that these conditions are not only necessary but also sufficient. In addition, sufficient conditions are derived such that the equivalent reduced-order system in the new sliding mode is asymptotically stable within the framework of linear matrix inequalities. A decentralized controller is synthesized to assure stability of the overall system. Finally, illustrative example is given to show the effectiveness of the proposed approach."

Keyword : Invariance condition, linear matrix inequality, mismatched uncertainty, variable structure systems.

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