非齐次Markovian跳变模糊系统的有限时间 H ∞控制

Finite-time H ∞ control for nonhomogeneous Markovian jump fuzzy systems

研究一类离散时间非齐次Markovian跳变奇异模糊系统的有限时间有界问题。在所有顶点已知的凸有界域内考虑时变的转移概率。首先,构造随机李雅普诺夫函数,引入矩阵变量给出奇异随机系统有限时间有界且具有H∞性能的充分条件,其中矩阵变量的结构不受限制,降低了保守性;其次,利用投影引理给出满足H∞性能的状态反馈控制器存在的线性矩阵不等式条件;最后,所提方法的可行性通过算例仿真得以验证。

The finite-time boundedness problem is investigated for discrete-time nonhomogeneous Markovian jump IT2 fuzzy systems.The time-varying transition probability is considered in the convex bounded domain with all vertices known.Firstly,by considering a stochastic Lyapunov function,the sufficient conditions for the finite time boundedness and H∞performance of singular stochastic systems are given by introducing specific matrix variables.Secondly,by using the projection lemma,the linear matrix inequality conditions for the existence of state feedback controllers satisfying the H∞performance level are given.Finally,an example is given to verify the effectiveness of the proposed theory.