Robust H filtering of stationary continuous-Time linear systems with stochastic uncertainties

E. Gershon, D. J.N. Limebeer, U. Shaked, I. Yaesh

Research output: Contribution to journalArticlepeer-review

159 Citations (Scopus)


The problem of applying H-filters on stationary, continuous-time, linear systems with stochastic uncertainties in the state-space signal model is addressed. These uncertainties are modeled via white noise processes. The relevant cost function is the expected value of the standard H performance index with respect to the uncertain parameters. The solution is obtained via a stochastic bounded real lemma that results in a modified Riccati inequality. This inequality is expressed in the form of a linear matrix inequality whose solution provides the filter parameters. The method proposed is also applied to the case where, in addition to the stochastic uncertainty, other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope. The problem of mixed H2/H filtering for the above system is also treated. The theory developed is demonstrated by a practical example.

Original languageEnglish
Pages (from-to)1788-1793
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number11
Publication statusPublished - Nov 2001
Externally publishedYes


  • Mixed H/H filtering
  • Polytopic uncertainty
  • Stochastic H filtering

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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