Stabilisation of commensurate fractional-order polytopic non-linear differential inclusion subject to input non-linearity and unknown disturbances

• Published in: IET control theory & applications Vol. 7; no. 12; pp. 1624 - 1633
• Main Authors: Abooee, Ali, Haeri, Mohammad
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.08.2013; John Wiley & Sons, Inc
• Subjects: Adaptation; adaptive control; bounded disturbance; closed loop systems; closed‐loop system; commensurate fractional‐order polytopic nonlinear differential inclusion; Computer simulation; control input; control nonlinearities; Control systems; dead‐zone nonlinearities; Disturbances; fractional‐order adaptive‐sliding mode control; Inclusions; input nonlinearity; Lyapunov methods; Lyapunov stability theorem; Mathematical models; nonlinear control systems; Nonlinearity; sector nonlinearities; SMC scheme; stabilisation; Stability; variable structure systems; SMC scheme; dead-zone nonlinearities; adaptive control; stabilisation; Lyapunov stability theorem; closed loop systems; sector nonlinearities; input nonlinearity; nonlinear control systems; control input; control nonlinearities; bounded disturbance; fractional-order adaptive-sliding mode control; stability; variable structure systems; commensurate fractional-order polytopic nonlinear differential inclusion; closed-loop system; Lyapunov methods
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2013.0038

In this study, a fractional-order adaptive-sliding mode control (SMC) scheme is proposed to stabilise commensurate fractional-order polytopic non-linear differential inclusion systems containing sector and dead-zone nonlinearities in the control inputs and unknown bounded disturbances. The suggested control method is composed of fractional-order sliding surfaces, adaptive-SMC inputs and adaptation laws for unknown bounds of disturbances. The Lyapunov stability theorem is used to prove the stability of the closed-loop system. A practical system and two numerical examples are simulated to show the effectiveness and performance of the proposed control technique.