Markov Jump Linear Systems

Abstract

Markov jump linear systems (MJLSs) is an important class of dynamic systems that has been deeply studied in the past years. The main reason is because MJLS models adequately, with precision, many practical applications of particular interest and importance. Nevertheless, concerning sampled-data control of MJLS, very few results are available in the literature. This chapter aims to design linear filters and controllers in both contexts of ${\mathcal {H}}_2$ and ${\mathcal {H}}_\infty$ performance optimization. As a by-product, several aspects of robust filtering and control are assessed and discussed. The same classes of filters and controllers are dealt with by generalizing the procedures already established in the previous chapters for deterministic dynamic systems. It is important to make clear that the stochastic nature of MJLS naturally reflects the need for more involved calculations to obtain the aforementioned performance indices as well as filter and control design conditions. In the Bibliography notes of this chapter useful information and references about Markov jump linear systems are provided and briefly discussed.