Non-fragile Control for Positive Markov Jump Systems with Actuator Saturation
This paper is concerned with the non-fragile control for a class of positive Markov jump systems in both continuous-time and discrete-time contexts. The systems under consideration are subject to actuator saturation and partially known transition probabilities. First, a stochastic co-positive Lyapunov function is constructed. Using the Lyapunov function, a set of mode-dependent state feedback control laws and attraction domain gains are designed based on a gain matrix decomposition technique. Furthermore, a cone is chosen as the attraction domain. The free weighting vectors are used to tackle incomplete transition probabilities. Sufficient conditions for non-fragile stochastic stability of the resulting closed-loop systems are developed by solving a linear programming problem. Compared with existing methods in the literature, the presented approach designs not only controller gains but also attraction domain gains with less conservativeness. Finally, two numerical examples are given to show the validity of the proposed approach.
KeywordsPositive Markov jump systems Actuator saturation Non-fragile controller Linear programming
The authors thank the anonymous reviewers and associate editor for their valuable suggestions and comments which have helped to improve the quality of the paper. This work was supported in part by the National Nature Science Foundation of China (61873314, 61503107, and U1509205), the Zhejiang Provincial Natural Science Foundation of China (S18F030001), and the Foundation of Key Laboratory of System Control and Information Processing, Ministry of Education, P.R. China.
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