Sliding-mode output feedback control design

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Abstract

We consider the sliding-mode output feedback controller (SMOFC) design problem for a class of uncertain multivariable 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 α-stability, LQ performance, H2/H performance, and peak-to-peak gain bound. In particular, we show that by including H 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.

Original languageEnglish
Pages (from-to)4047-4054
Number of pages8
JournalIEEE Transactions on Industrial Electronics
Volume55
Issue number11
DOIs
StatePublished - 2008

Keywords

  • Linear matrix inequality (LMI)
  • Output feedback
  • Sliding-mode control
  • Switching surface
  • Uncertain systems
  • Variable-structure system

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