ABSTRACT
This article on temporal analysis focuses more specifically on the principal properties of systems under their temporal aspects, that is to say their behavior according to the independent time variable. Evolutive Markov linear systems are detailed, notably state representations, the properties of the transition matrix or the nucleus of a linear system. Markov non-linear systems are then presented: evolutionary, permanent and separable systems. To conclude, explanations of temporal analysis (two degree of freedom, scalar and one degree of freedom master-slave systems) and temporal synthesis of master-slave systems are provided.
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INTRODUCTION
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 analysis is the subject of two dossiers [S7 150] Part 1 and [S7 151] Part 2, in which continuous, linear and permanent Markovian systems and their extensions to certain non-Markovian, non-linear or evolutionary systems are presented. Generally, we restrict our study to scalar systems, but whenever we can, we will provide the corresponding matrix systems, if these do not turn out to be much more complicated than the former. Finally, we have tried to illustrate each mathematical notion with practical applications taken from the world of engineering.
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Temporal analysis - Part 2