We always express our variables as function of time, x(t), for linear time-invariant systems we usually use Laplace transform to analyze them, for nonlinear and time-varying systems we use Lyapunov function to analyze the stability. Transforming our system from the time domain to s-domain creates complexity in our analysis, for example time delay systems becomes transcendental equation. My question is there any approaches or directions rather than transforming to frequency or complex frequency domains?
Dear Prof. Behnam thank you very much for your answer and I believe it will help me to focus on the time domain rather than the simplified transformations.
Best Regards,
Ashraf
Thank you very much Prof. Behnam the titles looks interesting for me specially the last reference:
[3] C Kuehn, Multiple Time Scale Dynamics (Springer, Heidelberg, 2015). Chapter 5.
Dear Ashraf Khalil
Please, see the ResearchGate discussion:
Equivalence of Laplace transform in frequency domain and time domain,
in the URL linked below:
https://www.researchgate.net/post/Equivalence_of_Laplace_transform_in_frequency_domain_and_time_domain
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