不确定离散半马尔可夫跳变系统的有限时间鲁棒$H_infty$控制

研究一类不确定离散时间半马尔可夫跳变系统的有限时间鲁棒H_∞控制问题.首先,应用半马尔可夫核方法建模离散时间系统的半马尔可夫跳变过程,其中驻留时间的概率密度函数依赖系统当前模态和下一模态,使得所提出理论可考虑不同的驻留时间概率分布类型,针对随机跳变系统有限时间分析中的跳变次数问题,提出估计跳变次数最大值的方法;然后,考虑系统模态驻留时间的上下界,提出新的有限时间有界概念,并保证基于半马尔可夫核方法给出的不确定离散时间半马尔可夫随机跳变系统有限时间有界判据数值可解;接着,在此基础上,分析系统的H_∞性能指标,设计模态依赖的状态反馈控制律保证闭环系统的有限时间鲁棒H_∞性能;最后,通过2个算例仿真验证所提出理论的可行性和有效性.

Robust finite-time $H_infty$ control for uncertain discrete-time semi-Markov jump systems

This paper studies the problem of robust finite-time $H_infty$ control for a class of uncertain discrete-time semi-Markov jump systems. The semi-Markov kernel approach is employed to model the semi-Markov jump process, in which the probability density function of sojourn time takes into account both the present and next system mode, and different types of sojourn time probability distribution can be considered in the proposed criteria. The method of estimating the maximum number of jumps is proposed for the finite-time analysis of the stochastic switching system. The upper and lower bound of sojourn time are considered simultaneously, which gives a novel concept of finite-time boundedness and guarantees the corresponding criteria based on the semi-Markov kernel to be numerically testable. On the basis of this concept, the $H_infty$ performance is studied and the corresponding design method of the mode-dependent state-feedback control law is given to guarantee the corresponding closed-loop system to be finite-time bounded with given $H_infty$ performance. Two numerical examples are delivered to illustrate the feasibility and effectiveness of the proposed theoretical method.