For an autonomous microgrid, the system does not have any external input or output variables as it is a self-contained system that operates independently. To obtain the state-space model for the microgrid, you need to determine the A matrix, which describes the behavior of the system in the absence of any input or output.

One approach to obtain the A matrix is to use the mathematical model of the microgrid that includes all the system components and their interactions. This mathematical model may be obtained through first-principles modeling or system identification techniques. Once the mathematical model is obtained, the A matrix can be extracted by neglecting the input and output variables.

Another approach is to use the small-signal model of the microgrid, which is a linear approximation of the system around its operating point. In this approach, you have to assume that the system is operating at a steady-state and small perturbations around this operating point can be modeled as linear. The A matrix can then be obtained by linearizing the system equations around the steady-state operating point.

To linearize the system, you can use the linearization function in MATLAB, which allows us to linearize the system without specifying the input and output variables. The function takes the system equations and the operating point as inputs and returns the A matrix.

In summary, to obtain the A matrix for an autonomous microgrid, you can either use the mathematical model or the small-signal linearized model. You can use the linearization function in MATLAB to linearize the system without specifying the input and output variables.