Families of solutions of matrix riccati differential equations

M. Pavon, D. D'Alessandro

Research output: Contribution to journalArticlepeer-review


The J. C. Willems-Coppel-Shayman geometric characterization of solutions of the algebraic Riccati equation (ARE) is extended to asymmetric Riccati differential equations with time-varying coefficients. The coefficients do not need to satisfy any definite-ness, periodicity, or system-theoretic condition. More precisely, given any two solutions X1(t) and X2(t) of such equation on a given interval [t0,t1], we show how to construct a family of solutions of the same equation of the form X(t) = (I - π(t))X1(t) + π(t)X2(t), where π is a suitable matrix-valued function. Even when specialized to the case of X1 and X2 equilibrium solutions of a symmetric equation with constant coefficients, our results considerably extend the classical ones, as no further assumption is made on the pair X1, X2 and on the coefficient matrices.

Original languageEnglish (US)
Pages (from-to)194-204
Number of pages11
JournalSIAM Journal on Control and Optimization
Issue number1
StatePublished - Jan 1997


  • Asymmetric Riccati differential equation
  • Families of solutions
  • Geometric characterization
  • Invariant subspaces
  • Projection-preserving differential equation

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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