转移概率部分未知时滞跳变系统有限时间控制

Finite-time control of time-delayed jumping systems with partial unknown transition probabilities

摘要:

时滞是许多工业系统的固有特性,会导致系统控制性能的下降,甚至影响系统稳定,而在实际系统中,有限时间系统的特性更值得关注。针对上述情况,对一类具有时滞的马尔可夫跳变系统有限时间控制器设计的问题进行了研究。把转移概率完全已知的条件放宽至部分未知的更一般情形,采用自由权重的方法,保证所得的线性矩阵不等式具有更小的保守性。首先,给出马尔科夫跳变系统有限时间有界性、有限时间 H无穷有界性的判定准则。然后,通过对线性矩阵不等式(LMIs)求解,获得状态观测器和状态反馈控制器的增益矩阵。最后,仿真实例验证所提算法的有效性。

Abstract:

Delay is an inherent characteristic of many industrial systems, which can lead to the decline of system control performance and even affect the stability of the system. In practical systems, the characteristics of finite-time systems deserve more attention. In view of the above situation, the design of finite-time controller for a class of Markov jump systems with time-delay is studied. By relaxing the condition that the transition probability is fully known to a more general case where the transition probability is partially unknown, the free weight method is adopted to ensure that the obtained linear matrix inequalities are less conservative. Firstly, the criteria of finite-time boundedness and finite-time Boundedness for Markov jumping systems are given. Then, the gain matrix of the state observer and the state feedback controller is obtained by solving the linear matrix inequality (LMIs). Finally, a simulation example is given to verify the effectiveness of the proposed algorithm.