Robust Stabilization Of Uncertain Markov Jump Linear Systems

In recent years, Markov jump linear systems have attracted many scholars due to its powerful background for practical application. Dynamic systems may suffer from many abrupt changes in their structures and parameters, which are often caused by component failures or repairs, abrupt environmental disturbances, or changing subsystem interconnections. That is to say, such systems would jump from one kind of mode to another different one. Markov jump linear systems can describe such a class of stochastic jump systems. The transitions between different modes are considered as random and are managed by a transition probability matrix which is called Markov chain. Because of these advantages of modeling of Markov jump linear systems, the study of the stability analysis of such systems is significant.In practice, most transition probability elements are hardly obtained which means Markov jump linear systems cannot shift among modes accordingly to the precise Markov chain in many practice situations. This dissertation describes a class of uncertain Markov jump linear systems with incomplete transition probability matrix in continuous-time and discrete-time domain respectively, discusses the stability and stabilization of such jump systems, and designs corresponding state-feedback controller to ensure the robust stochastic stability based on linear matrix inequation. The techniques introduced in this dissertation can not only be applied to the situation that the transition probabilities are partly unknown, but two extreme circumstances that the transition probabilities are fully known or completely unknown. Besides, the methods do not need any information of the probabilities. A large number of numerical examples illustrate that the states can quickly enter into the stable status, and the states do not change along with the transition once they become stable.Also, the observer-based control problems for Markov jump linear systems with uncertainties in continuous and discrete domain are investigated. Attention is focused on constructing a state observer and feedback controller to guarantee the closed-loop systems stable stochastically. Considering that many system states are unobservable, this method enlarges the application range of Markov jump linear systems. The numerical examples indicate the effectiveness of the theoretical results.