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研究一类带乘性噪声的离散时间随机Markov跳跃系统的有限时间控制问题.首先,定义系统的有限时间稳定和有限时间有界,通过逐次迭代和条件期望给出系统有限时间稳定的充分必要条件;其次,针对含干扰的系统,利用Lyapunov方法和线性矩阵不等式技术得到系统有限时间有界的充分条件并设计状态反馈镇定控制器;然后,进一步考虑转移概率信息不完全下的有限时间有界问题;最后,通过数值例子验证了所提出方法的有效性.
A finite time control problem for a class of discrete-time stochastic Markov jump systems with multiplicative noise is studied. First, the finite and bounded finite bounded systems are defined. The necessary and sufficient conditions for the finite-time system stability are given by successive iterations and conditional expectation Secondly, for the systems with interference, the sufficient conditions of the finite-time boundedness of the system are obtained by using the Lyapunov method and the linear matrix inequality technique and the state feedback stabilization controller is designed. Then, the finite-time bounded problem with incomplete transitional probability information is further considered Finally, the numerical results show the effectiveness of the proposed method.