Random stabilization of sampled-data control systems with nonuniform sampling

Authors:
Bin Tang;Qi-Jie Zeng;De-Feng He;Yun Zhang
Affiliations:
School of Automation, Guangdong University of Technology, Guangzhou, China 510006;School of Automation, Guangdong University of Technology, Guangzhou, China 510006;School of Automation, Guangdong University of Technology, Guangzhou, China 510006;School of Automation, Guangdong University of Technology, Guangzhou, China 510006
Venue:
International Journal of Automation and Computing
Year:
2012

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Abstract

For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is continuously distributed in a given interval, is described as a multiple independent and identically distributed (i.i.d.) process. With this process, the closed-loop system is transformed into an asynchronous dynamical impulsive model with input delays. Sufficient conditions for the closed-loop mean-square exponential stability are presented in terms of linear matrix inequalities (LMIs), in which the relation between the nonuniform sampling and the mean-square exponential stability of the closed-loop system is explicitly established. Based on the stability conditions, the controller design method is given, which is further formulated as a convex optimization problem with LMI constraints. Numerical examples and experiment results are given to show the effectiveness and the advantages of the theoretical results.