SMC Design for Robust Stabilization of Nonlinear Markovian Jump Singular Systems

• Published in: IEEE transactions on automatic control Vol. 63; no. 1; pp. 219 - 224
• Main Authors: Wang, Yueying, Xia, Yuanqing, Shen, Hao, Zhou, Pingfang
• Format: Journal Article
• Language: English
• Published: IEEE 01.01.2018
• Subjects: Aerodynamics; Fuzzy sliding surface; Integrated circuit modeling; Markovian jump singular systems (MJSS); Power system dynamics; Robustness; Sliding mode control; sliding-mode control (SMC); Stochastic processes; T–S fuzzy models; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2017.2720970

In this technical note, the sliding-mode control (SMC) problem is investigated for T-S fuzzy-model-based nonlinear Markovian jump singular systems subject to matched/unmatched uncertainties. To accommodate the model characteristics of such a hybrid system, a novel integral-type fuzzy sliding surface is put forward by taking the singular matrix and state-dependent projection matrix into account simultaneously, which is the key contribution of the note. The designed surface contains two important features: 1) local input matrices for different subsystems in the same system mode are allowed to be different; and 2) the matched uncertainties are completely compensated, and the unmatched ones are not amplified during sliding motion. Sufficient conditions for the stochastic admissibility of the corresponding sliding-mode dynamics are presented, and a fuzzy SMC law is constructed to ensure the reaching condition despite uncertainties. The applicability and effectiveness of our approach are verified by simulations on an inverted pendulum system.