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Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program

Research output: Contribution to journalArticle

  • G Li
  • Heath W. P.
  • Lennox B.
Original languageEnglish
Pages (from-to)554 - 563
Number of pages10
JournalIET Control Theory & Applications
Journal issue7
StatePublished - 2008


The stability of the feedback connection of a strictly proper linear time-invariant stable system with a static nonlinearity expressed by a convex quadratic program (QP) is considered. From the Karush-Kuhn–Tucker conditions for the QP, quadratic constraints that may be used with a quadratic Lyapunov function to construct a stability criterion via the S-procedure are established. The approach is based on existing results in the literature, but gives a more parsimonious linear matrix inequality (LMI) criterion and is much easier to implement. This approach can be extended to model predictive control and gives equivalent results to those in the literature but with a much lower dimension LMI criterion.

Additional information

Rose publication type: Journal article Terms of use: This paper is a postprint of a paper submitted to and accepted for publication in IET Control Theory & Applications and is subject to Institution of Engineering and Technology Copyright.

Research areas

  • absolute stability, lure systems, model predictive control

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