Robust Stochastic Stabilization for Positive Markov Jump Systems with Actuator Saturation
This paper is concerned with robust stochastic stabilization for positive Markov jump systems with actuator saturation. The considered systems contain interval and polytopic uncertainties, respectively. First, a stochastic co-positive Lyapunov functional is constructed for the systems. By virtue of the presented Lyapunov functional, a new controller design approach is addressed using matrix decomposition technique. Under the designed controller, robust stochastic stabilization of the systems with interval and polytopic uncertainties is achieved, respectively. Furthermore, an effective method for estimating the attraction domain is established by solving an optimization problem. An implemental algorithm is provided based on linear programming to solve the corresponding conditions. Finally, two numerical examples are provided to illustrate the reduced conservatism and effectiveness of the proposed design.
KeywordsPositive Markov jump systems Stabilization Actuator saturation Linear programming
The authors would like to express the most sincere gratitude to the anonymous reviewers for their valuable suggestions and comments to improve the quality of this paper. This work is supported by the National Natural Science Foundation of China under Grants 61503107, 61473107, and U1509205, the Zhejiang Provincial Natural Science Foundation of China under Grants LR16F030003, and the Cross-Discipline Innovation Team Building Project of Hangzhou Dianzi University.
- 1.M. Ait Rami, J. Shamma, Hybrid positive systems subject to Markovian switching, in Proceedings of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems (Zaragoza, Spain, 2009), pp. 138–143Google Scholar