Brief paper: Robust sampled-data H∞ control with stochastic sampling

Authors:
Huijun Gao;Junli Wu;Peng Shi
Affiliations:
Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, PR China;Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150001, PR China and Information and Electronic Technology Institute, Jiamusi University, Jiamusi, 15 ...;Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, United Kindom and School of Engineering and Science, Victoria University, Melbourne, Vic, 8001, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

In this paper, the problem of robust H"~ control is investigated for sampled-data systems with probabilistic sampling. The parameter uncertainties are time-varying norm-bounded and appear in both the state and input matrices. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input-delay approach, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters in the system matrices. By linear matrix inequality (LMI) approach, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an H"~ performance. Moreover, an H"~ controller design procedure is then proposed. An illustrative example is included to demonstrate the effectiveness of the proposed techniques.