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In this book, various singularly perturbed jump system models in continuous-time or discrete-time domain, such as Markov jump singularly perturbed systems, semi-Markov jump singularly perturbed systems, hidden Markov jump singularly perturbed systems, and singularly perturbed jump complex network model, have been considered for some control synthesis problems. Also, some partial probability information cases are taken into account when addressing those control synthesis problems. To show the effectiveness and applicability of the obtained results, some numerical examples and practical industrial model examples are given