Adaptive control of singular Markovian jump systems with uncertain switchings

This article studies the problem of adaptive control for a class of singular Markovian jump systems, upper bound of uncertain transition rates of which is unknown. Firstly, an adaptation law is developed to estimate the unknown parameter. Then, a new class of adaptive state feedback controller is proposed such that not only is the estimated error bounded in probability but also the states of the closed-loop system are asymptotically stable in probability. Moreover, the presented method is successfully extended to another general case that the transition rate matrix is partially unknown. Similarly, the bound of the unknown elements is not necessarily given beforehand. Finally, a numerical example is given to show the validity and superiority of the developed results.