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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 of a class of discrete-time inhomogeneous random Markov jump systems with multiplicative noise is studied. The transition probability matrix of the system is not a regular matrix but an interval matrix. Under the assumption of compactness of interval matrices, Then the sufficient and necessary conditions for the system to be stable for a finite time are given. Secondly, sufficient conditions for the finite-time system to be stable are obtained by using the Lyapunov method and the linear matrix inequalities, and the finite-time state feedback stabilization controller is designed. Finally, The simulation results show the effectiveness of the proposed method.