Control theory studies systems can be connected with other systems via inputs and outputs. The dynamics are often but not always described by differential or difference equations.

Because of its engineering motivations, control theory is often interested in detailed analysis results and design techniques. Other relevant areas of math include differential geometry, dynamical systems, probability, algebra, analysis, automata, complexity of algorithms, you name it. Control theorists and engineers are always looking to apply other mathematical techniques to their problems, so no one of them is control theory.

The terms you mentioned " "Lebesgue measure", "countable union" ", if you can elaborate which specific application you are considering then it would be more helpful for me to answer.

You can refer for control engineering:

Modern Control Engineering by Ogata

Control System Engineering by Nagrath Gopal

on Lebesgue measurement you need to understand it deeply, you can refer:

Lebesgue Measure and Integration: An Introduction by Frank Burk

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The following books are interesting

(1)Advanced Mathematical Tools for Automatic Control Engineers: Volume 2: Stochastic Systems (Advanced Mathematical Tools for Control Engineers)

Alex Poznyak

(2)Advanced Mathematical Tools for Control Engineers: Deterministic Systems

Alex Poznyak

(3)Modeling and Control of Complex Systems (Automation and Control Engineering)

Petros A. Ioannou, Andreas Pitsillides

The best way to have a complete understanding of these terms is to pick up a standard book of analysis like Walter Rudin's " Principles of mathematical analysis ." Hope this helps!

Dear Tanushree Roy ,

thanks for your help.