Journal
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
Volume 55, Issue 11, Pages 4047-4054Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIE.2008.2004386
Keywords
Linear matrix inequality (LMI); output feedback; sliding-mode control; switching surface; uncertain systems; variable-structure system
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Funding
- Dongguk University Research Fund
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We consider the sliding-mode output feedback controller (SMOFC) design problem for a class of uncertain multi-variable systems. We first design a stabilizing SMOFC for matched uncertain systems. Using linear matrix inequalities (LMIs), we derive a necessary and sufficient condition for the existence of a linear sliding surface depending on outputs and compensator states. Using the solution of the LMI existence condition, we characterize the gain matrices. We give the nonlinear switching feedback gain guaranteeing the reachability condition. Second, we give an LMI-based design method to combine various useful performance criteria which can be used to guarantee a desired robust performance in spite of mismatched uncertainties. The performance criteria include alpha-stability, LQ performance, H-2/H-infinity. performance, and peak-to-peak gain bound. In particular, we show that by including H-infinity performance constraints, we can easily solve the SMOFC design problem for challenging system models to which the previous methods are not easily applicable. Finally, we give a numerical design example showing that our method can be successfully applied to the problem of designing reduced-order SMOFCs for uncertain time-delay systems or mismatched uncertain systems.
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