Dear Sympy Community,
I hope you are all doing well. I am writing as a follow-up to my previous 
message regarding my interest in contributing to the sympy.physics.control 
module during GSoC 2025. I would like to share some further ideas and seek 
your feedback to ensure that my proposals align well with the project’s 
goals.

As mentioned on the project ideas page, I am interested in implementing the 
Z-transform for discrete time systems. 
In addition, I propose abstracting the concept of a transform for dynamic 
systems, which would encompass both the Z-transform for discrete time and 
the Laplace transform for continuous time. This abstraction should provide 
a unified framework for handling different types of systems more 
effectively.

Additionally, I propose the implementation of Horner’s algorithm to enhance 
polynomial evaluations within the module.

Furthermore, I am considering the addition of observability and 
reachability decompositions. My approach would involve developing these 
decompositions separately, as well as integrating Kalman’s decomposition 
where appropriate to further enhance the analysis of system dynamics.

I would greatly appreciate any feedback, suggestions, or guidance you may 
have regarding these ideas.
Thank you very much for your time and consideration.

Best regards,
Leonardo Mangani

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