> For the complete documentation index, see [llms.txt](https://nelson-9.gitbook.io/nelson/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://nelson-9.gitbook.io/nelson/markdown/en/control_system/dare.md).

# dare

Discret-time algebraic Riccati equation solution.

## 📝 Syntax

* \[X, L, G] = dare(A, B, Q)
* \[X, L, G] = dare(A, B, Q, R, S, E)

## 📥 Input argument

* A - Matrix representing the state with dimensions n x n, where n corresponds to the number of states.
* B - Matrix representing control with dimensions n x p, where p is the number of inputs.
* Q - Matrix describing the cost associated with the state, having dimensions n x n, where n is the number of states.
* R - Matrix representing the cost associated with control, with dimensions p x p, where p is the number of inputs.
* S - Matrix that is optionally real-valued with dimensions n x p.
* E - Matrix with dimensions n x n that serves as a descriptor matrix.

## 📤 Output argument

* X - stabilized solution for the discret-time Riccati equation of dimension n x n.
* L - Closed-loop pole vector.
* G - Gain matrix.

## 📄 Description

The function dare(A, B, Q) calculates the exclusive solution, denoted as X, for the discret-time algebraic Riccati equation with matrices A, B, and Q, and also provides additional matrices L and G.

## 💡 Example

```matlab
a = [-3 2;1 1];
b = [0 ; 1];
c = [1 -1];
r = 3;
[x, l, g] = dare(a, b, c'*c, r)

```

## 🔗 See also

[slicot\_sb02od](/nelson/markdown/en/slicot/slicot_sb02od.md), [slicot\_sg02ad](/nelson/markdown/en/slicot/slicot_sg02ad.md).

## 🕔 History

| Version | 📄 Description  |
| ------- | --------------- |
| 1.0.0   | initial version |