Brief paper: Passivity-based sliding mode control of uncertain singular time-delay systems

Authors:
Ligang Wu;Wei Xing Zheng
Affiliations:
Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, PR China;School of Computing and Mathematics, University of Western Sydney, Penrith South DC NSW 1797, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

In this paper the problem of sliding mode control (SMC) with passivity of a class of uncertain nonlinear singular time-delay systems is studied. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain singular time-delay system. By introducing some slack matrices, a delay-dependent sufficient condition is proposed in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive. The passification solvability condition is then established. Moreover, a SMC law and an adaptive SMC law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.