Lower-order H filter design for bilinear systems with bounded inputs

Edo Abraham*, Eric C. Kerrigan

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)


We propose an optimization-based method for designing a lower order Luenberger-type state estimator, while providing L2-gain guarantees on the error dynamics when the estimator is used with the higher order system. Suitable filter parameters can be computed by modelling the bilinear system as a linear differential inclusion and solving a set of bilinear matrix inequality constraints. Since these constraints are nonconvex, in general, we also show that one can solve a suitably defined semi-definite program to compute a bound on the level of suboptimality. The design method also allows one to explicitly take account of linear parameter uncertainties in order to provide a priori robustness guarantees. The H-infinity estimator not only has lower real-time computational requirements compared with a Kalman filter, but also does not require knowledge of the noise spectrum. For a numerical example, we consider the estimation of the radiation force for a wave energy converter, where a low-order model is used to approximate the radiation dynamics.

Original languageEnglish
Article number6996039
Pages (from-to)895-906
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number4
Publication statusPublished - 15 Feb 2015
Externally publishedYes


  • Bilinear systems
  • H-infinity filtering
  • LPV
  • Observers
  • Wave energy


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