Stabilization of Linear Systems Case

In this section, we consider the stabilization for semi-Markov jump singularly perturbed systems (SMJSPSs) subjected to partially available transition information. The considered system includes two special cases, that is, complete probability information case and partially unknown probability information case, which is more general. In addition, when dealing with the unknown part, all known information is fully utilized, thus the conservatism is reduced compared to the one that discard the known information. On this basis, some criteria ensuring the stochastic stability of the resulting SMJSPSs are derived. Furthermore, the controller design method under the agreed framework is established to ensure that the expected control effect can be achieved even when the dynamic state of the system is not available. Finally, this chapter concludes with a numerical example to demonstrate the validity of obtained results.