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access icon free Stability analysis of fractional order time-delay systems: constructing new Lyapunov functions from those of integer order counterparts

© The Institution of Engineering and Technology
Received 06/05/2018, Accepted 24/06/2019, Revised 27/04/2019, Published 25/06/2019

This study deals with proposing a Lyapunov-based technique for stability analysis of fractional order time-delay systems. The proposed technique is constructed on the basis of modifying the convex part of a class of Lyapunov–Krasovskii functionals commonly used in stability analysis of integer order time-delay systems. As a consequence for this achievement, it is revealed that the Lyapunov–Krasovskii-based stability conditions in integer order time-delay systems can result in stability of their fractional order counterparts defined based on Caputo/Riemann–Liouville derivative operators with orders in the range (0,1). The applicability of the study results is shown through three different case studies.

Inspec keywords: stability; delay systems; asymptotic stability; differential equations; time-varying systems; Lyapunov methods; linear systems; delays

Other keywords: stability analysis; fractional order counterparts; Lyapunov functions; Lyapunov-based technique; integer order time-delay systems; fractional order time-delay systems; integer order counterparts; Lyapunov–Krasovskii functionals; Lyapunov–Krasovskii-based stability conditions

Subjects: Control system analysis and synthesis methods; Linear control systems; Distributed parameter control systems; Function theory, analysis; Stability in control theory; Algebra

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