一类模糊双线性跳变系统的随机镇定问题

陈珺; 高泽峰; 刘飞

doi:10.3724/SP.J.1004.2013.00587

一类模糊双线性跳变系统的随机镇定问题

doi: 10.3724/SP.J.1004.2013.00587 cstr: 32138.14.SP.J.1004.2013.00587

1.
轻工过程先进控制教育部重点实验室江南大学自动化研究所无锡 214122

详细信息

通讯作者:
陈珺

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出版历程
- 收稿日期: 2012-05-15
- 修回日期: 2012-10-09
- 刊出日期: 2013-05-20

Stochastic Stabilization for a Class of Fuzzy Bilinear Jump Systems

1.
Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, Institute of Automation, Jiangnan University, Wuxi 214122

摘要

摘要: 研究了一类模糊双线性跳变系统的随机镇定问题. 采用T-S模糊建模技术来构建模糊双线性跳变模型, 然后通过并行分布补偿 (Parallel distributed compensation, PDC) 方法和选择合适的模糊隶属度函数, 将整个非线性控制器表示为一组局部线性控制器的模糊综合. 此外, 还推导出了保证闭环模糊双线性跳变系统随机稳定的充分条件, 并且这些条件最终可归结为一组线性矩阵不等式 (Linear matrix inequalities, LMIs)的可行性问题. 最后, 连续搅拌反应釜(Continuous stirred tank reactor, CSTR)系统的数值示例表明该设计方法的合理性和有效性.
- T-S模糊双线性模型 /
- 跳变参数 /
- 随机镇定 /
- 线性矩阵不等式 /
- 连续搅拌反应釜系统
Abstract: This paper deals with the problem of stochastic stabilization for a class of fuzzy bilinear systems with Markovian jump parameters. The Takagi-Sugeno (T-S) fuzzy modeling technique is adopted to construct a fuzzy bilinear jump model. By means of the parallel distributed compensation (PDC) method, an overall nonlinear controller is constructed by blending a set of local linear controllers through selected membership functions. Besides, some sufficient conditions are derived to guarantee the stochastic stability of the closed-loop fuzzy bilinear jump system via linear matrix inequalities (LMIs). Finally, a numerical example for a continuously stirred tank reactor (CSTR) system is given to illustrate the validity and effectiveness of the designed procedure.
- Takagi-Sugeno (T-S) fuzzy bilinear model /
- jump parameters /
- stochastic stabilization /
- linear matrix inequalities (LMIs) /
- continuously stirred tank reactor (CSTR) system

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参考文献(1)

[1]

Takagi T, Sugeno M. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 1985, 15(1): 116-132[2] Wang H O, Tanaka K, Griffin M F. Parallel distributed compensation of nonlinear systems by Takagi-Sugeno fuzzy model. In: Proceedings of the 4th IEEE International Conference on Fuzzy Systems and the Second International Fuzzy Engineering Symposium (FUZZ-IEEE/IFES). New York, USA: IEEE, 1995. 531-538[3] Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994. 7-35[4] Mohler R R. Bilinear Control Processes. New York: Academic, 1973[5] Elliott D L. Bilinear systems. Encyclopedia of Electrical Engineering. New York: Wiley, 1999[6] Mohler R R. Nonlinear Systems: Applications to Bilinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991[7] Li T H S, Tsai S H. T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems. IEEE Transactions on Fuzzy Systems, 2007, 15(3): 494-506[8] Li T H S, Tsai S H, Lee J Z, Hsiao M Y, Chao C H. Robust H∞ fuzzy control for a class of uncertain discrete fuzzy bilinear systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2008, 38(2): 510-527[9] Tsai S H. Robust H∞ control for van de vusse reactor via T-S fuzzy bilinear scheme. Expert Systems with Applications, 2011, 38(5): 4935-4944[10] Tsai S H, Li T H S. Robust fuzzy control of a class fuzzy bilinear systems with time-delay. Chaos, Solitons, and Fractals, 2009, 39(15): 2028-2040[11] Yoneyama J. Stabilization of Takagi-Sugeno fuzzy bilinear time-delay systems. In: Proceedings of the 2010 IEEE International Symposium on Intelligent Control. Yokohama, Japan: IEEE, 2010. 111-116[12] Chen T T, Tsai S H, Tsai K L, Li C L. Fuzzy control for T-S fuzzy bilinear systems with time-delay in state and control input. In: Proceedings of the 2011 International Conference on System Science and Engineering. Macau, China: IEEE, 2011. 346-351[13] Saoudi D, Mechmeche C, Benhadj Braiek N. T-S fuzzy bilinear observer for a class of nonlinear system. In: Proceedings of the 18th Mediterranean Conference on Control Automation Congress Palace Hotel. Marrakech, Morocco: IEEE, 2010. 1395-1400[14] Tsai S H, Chen T T, Hsiao M Y, Chen C S. Robust H∞ fuzzy observer for a class of time-delay discrete fuzzy bilinear systems with parameter uncertainties. In: Proceedings of the 2011 IEEE International Conference on Fuzzy Systems. Taipei, China: IEEE, 2011. 304-310[15] Feng X, Loparo K A, Ji Y, Chizeck H J. Stochastic stability properties of jump linear systems. IEEE Transactions on Automatic Control, 1992, 37(1): 38-53[16] Ji Y, Chizeck H J. Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Transactions on Automatic Control, 1990, 35(7): 777-788[17] Xu S Y, Lam J. Robust H∞ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers. IEEE Transactions on Fuzzy Systems, 2005, 13(1): 82-93

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