Research On Two Classes Of MARKOV Jump Linear Systems With Time-varying Transition Probability

Markov jump systems (MJSs) is a special and important class of stochastic hybrid systems due to the powerful modeling ability of Markov process in many fields, such as aerospace industry, communication systems, biology and medicine, economics, etc. Yet, so far, almost all the available analysis and synthesis results assume that the Markov processes or Markov chains in the underlying systems are time-invariant. However, the assumption is not true in practice. The existence of variations in transition probabilitys (TPs) challenges the traditional control approaches for the MJSs. So how to overcome the affect of variations in TPs is not only of theoretical but also of practical importance and is a complement to the available analysis and synthesis results on the MJSs.In this dissertation, we investigate the control and estimation problem for the Markov jump linear systems with time-varying TPs via two methods. The controbution of the dissertation is two fold:1. Improving the previous modeling method, we use siwtching signal to describle the vatiation of TPs. So the time-varying TPs is modeled as switching TP with the average dwell time constraint. Then, we investigate the undelying system by the theories on slow switching. Firstly, the less conservative stochastic stability criterion is obtained. Based on it, we get the design result of stabilization controller. Secondly, considering the underlying system with the disturbance, a Bounded Real Lemma (BRL) result is derived, upon which is built an H_∞control result and an H_∞estimation result for the system. The technique is illustrated by numerical examples and its use is exemplified with an application to an economic system model.2. Improving the previous control method, we assume the uncertain parameters in the uncertain TPs could be measured in real time. Using the parameter-dependent Lyapunov function, a less conservative stochastic stability criterion is derived. Then, based on the stability analysis result, a parameter-dependent stabilization controller is obtained. Then considering the underlying system with the disturbance, a Bounded Real Lemma (BRL) result is derived. By the BRL, we could built a parameter-dependent H_∞control result and a parameter-dependent H_∞estimation result for the underlying system. The superiority of the thoeretic results is demonstrated by numerical examples and its use is exemplified with an application to a solar thermal receiver.