State feedback stabilization of discrete linear switching systems subject to nonsymmetrical state and control bounds

• Published in: Journal of control theory and applications Vol. 10; no. 2; pp. 216 - 222
• Main Authors: Liu, Zhiyuan, Fan, Guowei, Chen, Hong
• Format: Journal Article
• Language: English
• Published: Heidelberg South China University of Technology and Academy of Mathematics and Systems Science, CAS 01.05.2012; Department of Control Science and Engineering, Harbin Institute of Technology, Harbin Heilongjiang 150001, China%Department of Control Science and Engineering, Jilin University, Changchun Jilin 130025, China
• Subjects: Complexity; Computational Intelligence; Control; Control and Systems Theory; Control systems; Controllers; Convergence; Design engineering; Engineering; Mechatronics; Optimization; Robotics; Stabilization; State feedback; Switching; Systems Theory; 控制输入; 最优收敛速度; 状态反馈控制器; 状态反馈镇定; 离散时间; 稳定性; 线性切换系统; 非对称; Stabilization problem; Convergence rate problem; Switching systems; Constraints
• ISSN: 1672-6340; 1993-0623
• DOI: 10.1007/s11768-012-0104-0

Stabilization problem of discrete-time linear switching systems with bounds on the state and control input is solved in this paper. First, the synthesis of state feedback controllers that ensure the stability of closed-loop switching systems is studied under a sufficient condition. By using the idea of positive invariance, a stabilizing controller design methodology is proposed. Based on these results, the convergence rate problem is also discussed. A state feedback controller that guarantees the optimal convergence rate of closed-loop switching systems is obtained via optimization. Finally, an example made up of two subsystems is studied to show the application of our method.