A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

• Published in: Journal of control theory and applications Vol. 9; no. 4; pp. 604 - 610
• Main Authors: Guan, Wei, Yang, Guanghong
• Format: Journal Article
• Language: English
• Published: Heidelberg South China University of Technology and Academy of Mathematics and Systems Science, CAS 01.11.2011; School of Automation, Shenyang Aerospace University, Shenyang Liaoning 110136, China%College of Information Science and Engineering, Northeastern University, Shenyang Liaoning 110004, China
• Subjects: Attraction; Complexity; Computational Intelligence; Construction; Control; Control and Systems Theory; Control systems; Design engineering; Dynamical systems; Dynamics; Engineering; Linear systems; Mechatronics; Optimization; Robotics; Saturation; Systems Theory; 状态反馈控制器; 离散时间; 稳定性分析; 线性系统; 设计方法; 设计问题; 输出反馈控制器; 饱和非线性; Linear systems; LMIs; State saturation
• ISSN: 1672-6340; 1993-0623
• DOI: 10.1007/s11768-011-9206-3

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ＇large＇ as possible. An example is provided to demonstrate the effectiveness of the new method.