Controllability and observability for fractal linear dynamical systems
Lakhlifa Sadek
Abstract
In the present paper, we investigate the controllability, and observability of a non-homogeneous continuous-time fractal dynamical system (NC-TFDS). We show that the controllability is equivalent to a controllability matrix that has a full rank. We also show a relationship between controllability and fractal differential Lyapunov equation (F-DLE). We give some theorems for the observability of a NC-TFDS. Finally, we offer two examples are provided to illustrate the effectiveness of our results and compare it with the two papers Al-Zhour (2022) and ( Sadek et al., 2022 ).
Topics & Concepts
ControllabilityObservabilityControl theory (sociology)MathematicsFractalNetwork controllabilityRank (graph theory)Applied mathematicsRank conditionDynamical systems theoryControllability GramianLyapunov functionDifferential (mechanical device)Topology (electrical circuits)Mathematical analysisPure mathematicsComputer scienceControl (management)Nonlinear systemPhysicsCombinatoricsArtificial intelligenceQuantum mechanicsCentralityBetweenness centralityThermodynamicsFractional Differential Equations SolutionsModel Reduction and Neural NetworksNeural Networks and Applications