A design of fuzzy sliding mode control for Markovian jumping system with different input matrices

• Published in: Applied mathematics and computation 2024-02, Vol.463, p.128372, Article 128372
• Main Authors: Zhang, Jianyu, Wang, Yingying, Yang, Songwei, Li, Jiaojiao, Qu, Hao
• Format: Article
• Language: English
• Subjects: Different local input matrices; Fuzzy systems; Markovian systems; Sliding mode control
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2023.128372

In this paper, by means of sliding mode control (SMC), the problem resulted by local input matrices is investigated for fuzzy markovian jumping system. The stability of the considered fuzzy Markovian system with multiple sub-input matrices can be fulfilled using the method in this paper. First, the state equation of the considered system is transformed according to the input matrices. Second, according to the state equation, sliding mode surface is constructed. This surface contains several sub-surfaces. It can deal with this kind of fuzzy Markovian system with multiple sub-input matrices and uncertainties. And another characteristic is that there is not the process of reaching the sliding mode surface; It can settle the problem resulted by Markovian jumping and sliding mode method together. Third, by use of the Cramer's rule, a criterion is provided to judge the existence of sliding mode dynamics equation. A controller containing several sub-controllers components is designed. And these sub-controllers should keep the considered system on the several sub-surfaces and not leave it. At last, simulations are provided to illustrate the validity of the method in this paper.