Finite-time boundedness and finite-time stabilization boundedness for nonlinear interconnected systems with Atangana–Baleanu–Caputo fractional derivative

Dinh Cong Huong

2023Transactions of the Institute of Measurement and Control10 citationsDOI

Abstract

In this paper, we consider the finite-time boundedness (FTB) and finite-time stabilization boundedness (FTSB) problems for a class of nonlinear interconnected systems with Atangana–Baleanu–Caputo (ABC) fractional derivative. By employing the FTB theory and some properties of ABC fractional derivative, and some basic mathematical transformations, we derive new conditions for the FTB and FTSB problems of ABC fractional-order nonlinear interconnected systems. These conditions are formed in linear matrix inequalities (LMIs), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, two numerical examples with simulations are provided to illustrate the efficiency of the proposed method.

Topics & Concepts

Nonlinear systemMathematicsFractional calculusControl theory (sociology)MATLABApplied mathematicsClass (philosophy)Derivative (finance)Mathematical optimizationControl (management)Computer sciencePhysicsArtificial intelligenceQuantum mechanicsEconomicsOperating systemFinancial economicsFractional Differential Equations SolutionsAdvanced Control Systems DesignMatrix Theory and Algorithms