Abstract
This chapter studies the constrained regulation problem for a class of singular S-MJS. Using a supplementary variable technique and a plant transformation presented in Chap. 1, a finite PH semi-Markov process has been transformed into a finite Markov chain, which is called its associated Markov chain. Then, the S-MJS of this kind has been transformed into its associated Markovian system. Motivated by recent develops in positively invariant set, necessary and sufficient conditions for the existence of full rank solutions for a class of nonlinear equations are derived, and a new algorithm that provides a solution to the constrained regulation problem is presented.
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Li, F., Shi, P., Wu, L. (2017). Constrained Regulation of Singular Semi-Markovian Jump Systems. In: Control and Filtering for Semi-Markovian Jump Systems. Studies in Systems, Decision and Control, vol 81. Springer, Cham. https://doi.org/10.1007/978-3-319-47199-0_3
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DOI: https://doi.org/10.1007/978-3-319-47199-0_3
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