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I'm Trying to help in this question which involves Algebraic Ricatti equation. Honestly to say I never met this equation before.

I'm struggling to understand the conditions stated in the limitations of the dare algorithm in matlab. For convinience I quote it here:

The $(A, B)$ pair must be stabilizable (that is, all eigenvalues of $A$ outside the unit disk must be controllable). In addition, the associated symplectic pencil must have no eigenvalue on the unit circle. Sufficient conditions for this to hold are $(Q, A)$ detectable when $S = 0$ and $R > 0$, or $$\begin{bmatrix} Q & S \\ S^T & R \end{bmatrix}>0$$

All $A,B,S$ are matrices ($S=0$ in my case ), so I don't understand how a matrix can be greater then zero? Is this is special notations for positive definite matrix?

Community
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Michael Medvinsky
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1 Answers1

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This is just a notation for positive definite matrix. Several works use this $>$ instead of $\succ$. In the context of control theory both notations mean the same thing.

AndyOak
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  • are you familiar with $dare$ by mistake? I tried to create random $R,Q$ with eigenvalues $>0$ together with controllable $(A, B)$ but $dare$ still fails $70%$ of times which make me craze:( Where am I wrong? – Michael Medvinsky Dec 11 '15 at 17:27
  • Try making sure they are symmetric. It could help the solver. – AndyOak Dec 14 '15 at 15:22
  • look at the code under the link in the question please. It missing the part where I make sure the eigenvalues are positive, but for this part I do something very stupid-simple like stay in a loop until it so. – Michael Medvinsky Dec 14 '15 at 15:44