Abstract
As one of the most important control problems, the stabilization problem is to design a controller such that the corresponding closed-loop system is stable and has desired performances. Due to singular Markovian jump systems containing singular derivative matrix and Markov property simultaneously, the control synthesis of stabilization of the SMJSs becomes complex especially when the underlying SMJSs have some general conditions. In this chapter, stabilization problem of SMJSs is focused and controllers are to be designed such that the closed-loop system is regular, impulse-free and stable. A robust stabilizing controller guaranteeing the closed-loop systems robustly stochastically admissible is designed based on LMI techniques. When a TRM can be designed, the stabilization for SMJSs is also discussed. Various controllers based on noise control, proportional-derivative (PD) control and partially mode-dependent (PMD) control, are proposed. These controllers are formulated in terms of LMIs or LMIs with equation constraints, which can be solved easily.
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Wang, G., Zhang, Q., Yan, X. (2015). Stabilization. In: Analysis and Design of Singular Markovian Jump Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-08723-8_3
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DOI: https://doi.org/10.1007/978-3-319-08723-8_3
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