Time analysis — Part 1

Under the heading temporal analysis, we examine the main properties of systems in their temporal aspects, i.e. their behavior as a function of the independent variable called time t. This presentation focuses on continuous, linear and permanent Markovian systems, and their extensions to certain non-Markovian, non-linear or evolutionary systems. In general, we restrict our study to scalar systems, but whenever possible, we will provide the corresponding matrix systems, if these do not turn out to be much more complicated than the former. Deliberately, we remain silent about sampled systems. Indeed, to be able to say anything intelligent about the temporal behavior of such systems, we would first have to examine discrete systems theory in detail. This theory alone would require a dossier. Hence our decision to say nothing on the subject.

Finally, we have tried to illustrate each mathematical notion with practical applications taken from the world of engineering.

This temporal analysis is the subject of two files: [S 7 150] Part 1 and Part 2.