Abstract
The stabilization conditions of the discrete Takagi–Sugeno (T–S) fuzzy system are reduced by considering possible switching subregions. In addition, the stabilization conditions for the T–S fuzzy system are relaxed by representing the interactions among the fuzzy subsystems in a single matrix. However, these two concepts have not been applied together to the discrete T–S fuzzy system with constraints on the control input. The aim of this paper is to relax the stabilization conditions for the discrete T–S fuzzy system with constraints on the control input. The possible switching subregions fired by two successive states of the system are analyzed and utilized to reduce the stabilization conditions. The interactions of fuzzy subsystems within two subregions are integrated into a single matrix to relax the stabilization conditions. The relaxation and effectiveness of the proposed stabilization conditions are demonstrated by a numerical example and a mass-spring-damper system.
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