广义Markovian跳变系统, 作为广义系统重要组成部分，由于考虑了随机跳变的影响，更具应用背景和理论研究意义。但是由于随机跳变和奇异摄动的引入增加了系统结构的复杂性，广义Markovian跳变系统的研究仍存在许多基本问题亟待解决。本项目将针对几类广义Markovian跳变系统研究其建模与控制方法问题。主要研究内容如下：利用生物经济平衡现象和价格参数的Markov特性提出一类时滞广义生物经济Markovian跳变模型，将该模型用T-S模糊系统近似并研究其控制方法；采用增广矩阵的方法研究T-S模糊广义Markovian跳变系统的有限时间控制问题；基于积分型滑模函数，研究广义Markovian跳变系统的滑模控制方法；基于非积分型滑模函数，研究伊藤型广义随机Markovian跳变系统的自适应滑模控制方法。以上研究将为广义Markovian跳变系统理论和应用提供有效的方法和可行的新思路。

As an important part of singular systems, singular Markovian jump systems take into account the factor of random jump effects, thus are more applicable and have great significance of theoretical study. Since the introduction of the random jump and the singular perturbation makes the system structure more complex, singular Markovian jump systems deserve the further investigation. For some kinds of singular Markovian jump systems, this project proposes some new models and studies new control methods. Firstly, a class of singular bio-economic Markovian jump models with time delay is established by the bio-economic balance and the Marrkov characteristic of the price parameter, then the models are approached by T-S fuzzy systems and the control methods are studied. Secondly, the finite-time control for T-S fuzzy singular Markovian jump systems is developed on the basis of the augmented matrix. Thirdly, based on the integral type sliding mode function, this project investigates the sliding mode control method for singular Markovian jump systems. Lastly, based on the non-integral type sliding mode function, this project also investigates the adaptive sliding mode control method for Ito type singular stochastic Markovian jump systems. Through the above study, effective methods and new feasible ideas are provided for the theory and applications of singular Markovian jump systems.