带乘性噪声的非齐次Markov跳跃系统有限时间稳定性

Finite-time stability for nonhomogeneous Markov jump systems with multiplicative noises

研究一类带乘性噪声的离散时间非齐次随机Markov跳跃系统的有限时间稳定性,该系统的转移概率矩阵不是常矩阵而是区间矩阵.在区间矩阵紧性的假设下,将其表示为随机矩阵的凸组合.首先,给出系统有限时间稳定的充分必要条件;其次,利用Lyapunov方法和线性矩阵不等式技术得到系统有限时间稳定的充分条件,并用于设计有限时间状态反馈镇定控制器;最后,通过仿真算例说明所提出方法的有效性.

The finite-time stability for a class of discrete-time stochastic Markov jump systems with multiplicative noises is studied. The transition probability matrix is not a constant matrix but a interval matrix. Under the assumption of the compactness of the interval matrix, it is represented as a convex combination of some random matrices. Firstly, the sufficient and necessary condition of finite-time stability is given. Then, a sufficient condition for the finite-time stability of the system is obtained and the finite-time stabilization controller with state feedback is designed by using the Lyapunov method and linear matrix inequality technique. Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.