A comparison theorem for matrix Riccati difference equations

Harald K. Wimmer, Michele Pavon

Research output: Contribution to journalArticlepeer-review


Difference equations of the form X(t) = F*(t)X(t - 1)F(t) - F*(t)X(t - 1)G(t)[I + G*(t)X(t - 1)G(t)-1G*(t)X(t - 1)F(t) + Q(t) and their associated Hermitian matrices H(t) = (FQF*-GG *)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to the discrete-time LQ optimal control problem is given.

Original languageEnglish (US)
Pages (from-to)233-239
Number of pages7
JournalSystems and Control Letters
Issue number3
StatePublished - Sep 1992


  • discrete-time LQ optimal control
  • Matrix Riccati difference equations
  • monotonicity of solutions

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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