Game theoretic approach to H control for time-varying systems

David J.N. Limebeer, Brian D.O. Anderson, Pramod P. Khargonekar, Michael Green

Research output: Contribution to journalArticlepeer-review

132 Citations (Scopus)


A representation formula for all controllers that satisfy an L-type constraint is derived for time-varying systems. It is now known that a formula based on two indefinite algebraic Riccati equations may be found for time-invariant systems over an infinite time support (see [J.C. Doyle et al., IEEE Trans. Automat, Control, AC-34 (1989), pp. 831-847]; [K. Glover and J.C. Doyle, Systems Control Lett., 11 (1988), pp. 167-172]; [K. Glover et al., SIAM J. Control Optim., 29 (1991), pp. 283-324]; [M. Green et al, SIAM J. Control Optim., 28 (1990), pp. 1350-1371]; [D.J.N. Limebeer et al., in Proc. IEEE conf. on Decision and Control, Austin, TX, 1988]; [G. Tadmor, Math. Control Systems Signal Processing, 3 (1990), pp. 301-324]). In the time-varying case, two indefinite Riccati differential equations are required. A solution to the design problem exists if these equations have a solution on the optimization interval. The derivation of the representation formula illustrated in this paper makes explicit use of linear quadratic differential game theory and extends the work in [J.C. Doyle et al., IEEE Trans. Automat. Control, AC-34 (1989), pp. 831-847] and [G. Tadmor, Math. Control Systems Signal Processing, 3 (1990), pp. 301-324]. The game theoretic approach is particularly simple, in that the background mathematics required for the sufficient conditions is little more than standard arguments based on 'completing the square.'

Original languageEnglish
Pages (from-to)262-283
Number of pages22
JournalSIAM Journal on Control and Optimization
Issue number2
Publication statusPublished - 1992
Externally publishedYes

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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