Properties Of Linear Time-invariant Systems Research Articles

Algebraic analysis of the structural properties of parametric linear time‐invariant systems

By using techniques borrowed from algebraic geometry, some tests are proposed to certify structural properties (such as reachability, observability, controllability, constructibility, stabilisability, and detectability) of discrete-time and continuous-time linear time-invariant systems. These results are then generalised for linear time-invariant systems depending polynomially on some real parameters, by exploiting the notion of Gröbner cover. The main innovation of the proposed results with respect to existing techniques is that they provide exact certificates for the structural properties of linear time-invariant systems. Examples of application are given all throughout the study to illustrate and validate the theoretical results.

Positive real and strictly positive real MIMO systems: theory and application

The paper is dealing with the concept of positive real and strictly positive real properties of linear time-invariant systems. Although strict positive realness is the most important subset of positive real systems and extensively used in stabilizing control systems, there are inconsistencies in the literature for its necessary and sufficient conditions. Also, many frequency properties of such systems are less attended by the scholars. In this paper, a comprehensive discussion on definitions, properties, lemmas, and theorems related to multi-input multi-output positive real and strictly positive real systems will be presented. Further, several frequency domain properties are presented to characterize these functions. Also, three equivalent high frequency condition presented in the literature for strictly positive real systems are compared. The main results have been supported via several illustrative examples.

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

ABSTRACTStructural 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.