# Create 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.

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

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

Create the tunable parameters using realp.

a = realp('a',-1);
b = realp('b',3);

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 [1 2;0 -3], from the initial values of a and b.

Create the fixed-value state-space matrices.

B = [-3.0;1.5];
C = [0.3 0];
D = 0;

Use ss to create the state-space model.

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

Generalized continuous-time state-space model with 1 outputs, 1 inputs, 2 states, and the following blocks:
a: Scalar parameter, 2 occurrences.
b: Scalar parameter, 2 occurrences.

Type "ss(sys)" to see the current value, "get(sys)" to see all properties, and "sys.Blocks" to interact with the blocks.

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