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## State-Space Model with Both Fixed and Tunable Parameters

This example shows how to create a state-space (genss) model having both fixed and tunable parameters.

Create a state-space model having the following state-space matrices:

$A=\left[\begin{array}{cc}1& a+b\\ 0& ab\end{array}\right],\text{ }B=\left[\begin{array}{c}-3.0\\ 1.5\end{array}\right],\text{ }C=\left[\begin{array}{cc}0.3& 0\end{array}\right],\text{ }D=0,$

where a and b are tunable parameters, whose initial values are –1 and 3, respectively.

1. Create the tunable parameters using realp.

``` a = realp('a',-1);
b = realp('b',3);```
2. Define a generalized matrix using algebraic expressions of a and b.

`A = [1 a+b;0 a*b]`

A is a generalized matrix whose Blocks property contains a and b. The initial value of A is M = [1 2;0 -3], from the initial values of a and b.

3. Create the fixed-value state-space matrices.

```B = [-3.0;1.5];
C = [0.3 0];
D = 0;```
4. Use ss to create the state-space model.

`sys = ss(A,B,C,D)`

sys is a generalized LTI model (genss) with tunable parameters a and b.

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