Introduction and Preview

The coexistence of multiple-time scales dynamics phenomena and sudden changes in system structure and parameters are frequently encountered in engineering control systems. Generally, these control systems can be well modeled as singularly perturbed jump systems. During the past decades, as a class of singularly perturbed jump systems, Markov jump singularly perturbed systems have been rapidly developed and some control synthesis problems of such singularly perturbed jump systems have attracted more and more attention by many scholars, while other complex singularly perturbed jump system have been rarely considered, in which the other complex jump cases may include the sudden changes in system structure and parameters modeling by semi-Markov process and hidden Markov process. In this chapter, an introduction and preview of singularly perturbed jump systems is presented.