Hi, I think the largest Lyapunov exponent would be a really good option to evaluate your system stability if you have the model of your dynamical system.

Take a look at the following paper:

Article Surrogate model approach for investigating the stability of ...

You can find the codes to adapt such an algorithm to your particular case study here:

https://github.com/FuhgJan/AdaptiveMIVor

Thanks, Dr. Humberto I downloaded the paper and the code. I just want to make sure that the point of not having an s-domain model is considered in your answer. I just have a Simulink model that is simply processing numerical inputs to give the numerical outputs. However, it is dynamic. The frequency of the inputs can change with time and consequently, the outputs will change

Hi Prof. Osama Arafa,

If you possess some knowledge of the electrical/energy system to be controlled, then there must be some governing equations that describe the generic classes of such system. With sufficient input-output data, you can apply system identification techniques to determine the nominal values of the unknown parameters of the system. Having the nominal values, you can create an uncertain mathematical model for the electrical/energy system for robust stability analysis.

Otherwise, you may need to use the meticulous graphical approach to find out the stabilizing regimes of the control inputs, and to verify the system stability for the entire operating range of the control system.

Hi, the computation of the largest Lyapunov exponent just requires a time series. You don't need the representation of your system in the frequency domain to perform the stability analysis. Additionally, it doesn't matter whether your system is nonlinear. You could use your Simulink model as a black-box model then analyze the system stability based on the input-output response.

Hi Dr. Chak,

Thank you for your answer. It will be highly appreciated if you can support further (if possible, please examine the attached Simulink file in Matlab208A format).

My algorithm (the block with light-blue background) receives three-phase bipolar signals in addition to a fourth slowly changing positive signal. The frequency of the three-phase signal may change between zero and a known upper bound (changing rate is limited to a finite limit as well). The algorithm's objective is to continually track the phase angle of the input three-phase signals. By stability is meant, the algorithm can keep tracking of the phase angle of the input signals infinitely!

The process within the algorithm is highly nonlinear and as I said only the Simulink numerical model is available (attached)