Integrator‐based robust H∞ sliding mode control of uncertain stochastic Markovian jump delay systems with non‐linear perturbations

• Published in: IET control theory & applications Vol. 11; no. 8; pp. 1124 - 1133
• Main Authors: Jiang, Baoping, Kao, Yonggui, Gao, Cunchen
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 12.05.2017
• Subjects: asymptotic stability; closed loop systems; control system synthesis; delay systems; H∞ control; integral sliding surface functional; integrator‐based robust H∞ sliding mode control; linear matrix inequalities; linear matrix inequalities technique; nonlinear control systems; nonlinear perturbations; novel sliding mode controller design; parameter uncertainties; perturbation techniques; prescribed disturbance attenuation level; resulting closed‐loop system; robust control; robust mean‐square exponential stability; stochastic systems; system trajectories; uncertain stochastic Markovian jump delay systems; uncertain systems; variable structure systems
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2016.0841

This study is concerned with the problem of robust H∞ sliding mode control (SMC) of It o^ stochastic delayed Markovian jump systems subject to parameter uncertainties and non‐linear perturbations. Firstly, for the sake of practicality, a common integral sliding surface functional without time‐varying delay is proposed. Then, by using linear matrix inequalities technique, sufficient condition for the robust mean‐square exponential stability of the resulting closed‐loop system with a prescribed disturbance attenuation level γ is derived. Moreover, a novel sliding mode controller is designed such that system trajectories can be kept on the sliding surface almost surely since the initial time. Finally, an example is provided to illustrate the effectiveness of the obtained result.