Positivity and stability of mixed fractional‐order systems with unbounded delays: Necessary and sufficient conditions
Hoang The Tuan, Hieu Trinh, James Lam
Abstract
Summary This article provides a comprehensive study on quantitative properties of linear mixed fractional‐order systems with multiple time‐varying delays. The delays can be bounded or unbounded. We first obtain a result on existence and uniqueness of solutions to these systems. Then, we prove a necessary and sufficient condition for their positivity. Finally, we provide a necessary and sufficient criterion to characterize asymptotic stability of positive linear mixed fractional‐order systems with multiple time‐varying delays.
Topics & Concepts
UniquenessBounded functionMathematicsStability (learning theory)Order (exchange)Applied mathematicsExponential stabilityLinear systemControl theory (sociology)Nonlinear systemComputer scienceMathematical analysisControl (management)FinanceArtificial intelligenceQuantum mechanicsPhysicsEconomicsMachine learningAdvanced Control Systems DesignFractional Differential Equations SolutionsAdvanced Differential Equations and Dynamical Systems