The study of structural properties of linear time-invariant systems and their dependability: a Monte Carlo simulation approach

Structural properties such as the controllability and observability are of major importance in automatic control. Indeed, the controllability property of a system, for example, guarantees that this system can be controlled to carry out the specified mission it is designed for. These properties rely on the system's structure and components more than the numerical value of its internal parameters. However, these may be prone to failures that can make the system lose its initial properties, thus affecting its function. This paper proposes to use the Monte Carlo simulation and Kalman algebraic criteria to study the generic controllability and observability of linear time-invariant systems represented by structured models. The proposed approach allows, on the one hand, to compute the set of components which are necessary for these structural properties and, on the other hand, to assess the dependability of these properties.