Predictor-based control of systems with state multiplicative noise

E. Gershon, E. Fridman, U. Shaked

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21 Scopus citations


The problem of H∞ state-feedback control of linear continuous-time systems with state multiplicative noise in the presence of input delay is investigated. A predictor-based control is applied, for the first time, to these systems. A new condition for stability is derived in a form of a linear matrix inequality. The latter condition is extended to one that guarantees a prescribed L2-gain bound for the stochastic system. Solutions are obtained for both constant and time-varying delays. Because of the multiplicative noise, the predictor-based control cannot stabilize the system for arbitrarily large delay. It admits, however, delays that are significantly larger than the delays that can be treated by the corresponding non-predictive state-feedback control. The theoretical results are demonstrated by two examples. The first example shows the advantage of the predictor-based controller and the second one demonstrates the applicability of the theory to process control systems.

Original languageEnglish
Article number7519082
Pages (from-to)914-920
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - Feb 2017


  • Predictor-control
  • stochastic
  • time-delay


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