MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Greetings to members here. The question is how to calculate the solution $S(k)$ of the following recursive equation $$J(k)S(k+1)J^{T}(k)=A(k)S(k)A^{T}(k)+R(k)$$ where $J$ and $A$ are rectangular not square. $R$ is positive-definite. Furthermore, $J$ and $A$ are with full-row rank.

share|cite|improve this question
What is the source of this problem? Looks a lot like a discrete-time difference Riccati equation. This, and what Robert Israel said. – Federico Poloni Apr 21 '13 at 11:13
This is a Lyapunov equation. We met with the problem for treating desciptor system with white noise. $$J(k)x(k+1)=A(k)x(k)+w(k)$$ – eolithr Apr 22 '13 at 12:51
up vote 2 down vote accepted

If $J$ has more columns than rows, the map $S \to J S J^T$ is not one-to-one, so your equation does not determine $S(k+1)$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.