Stabilization

As one of the most important control problem, the stabilization problem is to design a controller such that the closed-loop system will be stable and has some desired performances. Due to singular Markovian jump systems containing singular derivative matrix and Markov property simultaneously, they usually complicate the synthesis, especially the underlying SMJSs have some general conditions. In this chapter, we will focus on the stabilization problem of SMJSs. Some kinds of

controllers such that the closed-loop system is regular, stable and impulse-free are designed. A robust stabilizing controller guaranteeing the closed-loop systems robustly stochastically admissible is designed in the LMI setting. When an TRM can be designed, the stabilization for SMJSs is also discussed. The other kinds of controllers realized by noise control, proportional-derivative (PD) control and partially mode-dependent (PMD) control are put forward. Such stabilizing controller designs are formulated in terms of LMIs or LMIs with equation constraints, which can be solved easily.