Linear systems with multiplicative noise: Discrete-time H tracking with preview

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Citations (Scopus)


The problem of finite-horizon H tracking for linear time-varying systems with stochastic parameter uncertainties is investigated. We consider three tracking patterns depending on the nature of the reference signal i.e : whether it is perfectly known in advance, measured on line or previewed in a fixed time-interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices of the system. For each of the above three cases a game theory approach is applied where, given a specific reference signal, the controller plays against nature which chooses the initial condition and the energy-bounded disturbance. The problems are solved using an expected value of the standard performance index over the stochastic parameters, where necessary and sufficient conditions are found for the existence of a saddle-point equilibrium. The infinite-horizon time-invariant tracking problem is also solved. The theory developed is demonstrated by a simple example.

Original languageEnglish
Title of host publication2001 European Control Conference, ECC 2001
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9783952417362
Publication statusPublished - 2001
Externally publishedYes
Event6th European Control Conference, ECC 2001 - Porto, Portugal
Duration: 4 Sept 20017 Sept 2001

Publication series

Name2001 European Control Conference, ECC 2001


Conference6th European Control Conference, ECC 2001


  • LMI
  • preview tracking
  • Stochastic H
  • stochastic uncertainty
  • tracking

ASJC Scopus subject areas

  • Control and Systems Engineering


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