部分转移概率未知的非线性马尔科夫跳变系统的H_∞控制

H_∞ Control for Markov Jump Systems With Partially Unknown Transition Probabilities and Nonlinearities

研究了一类含有未知转移概率的非线性马尔科夫跳变系统的H∞控制问题.所研究的系统具有如下新特性:首次对非线性函数在约束界内的内部变化规律加以利用;马尔科夫跳变系统的部分转移概率完全未知.当处理未知转移概率时,充分利用了未知转移概率和已知转移概率之间的关系.通过对以上新特性进行建模,得到了更具一般性的非线性马尔科夫跳变系统模型.对该模型应用李雅普诺夫函数法,得到了系统均方渐近稳定条件.最后给出的数值算例表明:首先,未知和已知转移概率关系的利用减少了结果的保守性;其次,非线性函数新特性的使用极大地改善了系统的控制性能.

This paper studies the H∞ controller design for Markov jump systems with partially unknown transition probabilities and nonlinearities.The studied systems have the following new characters： 1） the inner variation information of the nonlinear function between the bounds is firstly utilized to analysis the nonlinear function;2） some of the transition probabilities are completely unknown,and full use is made of the relationship between the known and unknown transition probabilities to analyze the Markov jump system.With Lyapunov function method,sufficient conditions for mean square stability of the system can be obtained.The finial numerical example shows that,firstly,the usage of the relationship between known and unknown transition probabilities can reduce the conservatism of the results,and that,secondly,the utilization of the new characters of the nonlinearities can improve the control performance of the system greatly.