Antidisturbance Control Design for Interval Type-2 Fuzzy Stochastic Systems With Input Quantization

Quantized antidisturbance control design problem is presented for a class of interval type-2 (IT2) fuzzy stochastic systems subject to time delays and multiple disturbances. The inherent uncertain nonlinear and hybrid characteristics of the concerned system make it difficult to design a stable antidisturbance controller. In order to properly reflect the characteristics of IT2 fuzzy stochastic models with multiple disturbances, a new fuzzy disturbance observer is proposed to estimate the disturbances generated by a fuzzy exogenous system. Furthermore, a quantized fuzzy antidisturbance control scheme is synthesized by fusing the estimation of the multiple disturbances. With the support of Lyapunov functional method, Ito's formula and auxiliary function-based integral inequality, the resulting IT2 fuzzy stochastic systems are proved to be robustly stochastically stable with mixed H-infinity/passivity performance index. The design methods of the fuzzy disturbance observer and quantized antidisturbance controller are formulated in the form of linear matrix inequalities so that the corresponding gain matrices can be easily obtained. Finally, simulation studies on three examples are provided to justify the efficiency of the designed control strategy.

Automated summary

This paper presents a quantized antidisturbance control design problem for a class of interval type-2 (IT2) fuzzy stochastic systems subject to time delays and multiple disturbances. Due to the inherent uncertain nonlinear and hybrid characteristics of the system, designing a stable antidisturbance controller becomes difficult. To properly reflect the characteristics of IT2 fuzzy stochastic models with multiple disturbances, a new fuzzy disturbance observer is proposed. A quantized fuzzy antidisturbance control scheme is then synthesized by fusing the estimation of the multiple disturbances. With the support of Lyapunov functional method, Ito's formula, and auxiliary function-based integral inequality, the resulting IT2 fuzzy stochastic systems are proved to be robustly stochastically stable with mixed H-infinity/passivity performance index. The design methods are formulated using linear matrix inequalities for easy obtainment of gain matrices. Simulation studies on three examples justify the efficiency of the designed control strategy.