基于一种分段泛函的马尔可夫跳变系统的采样控制

马尔可夫跳变系统（MJSs）是实际应用中一种极其重要的混合随机系统,本文研究了MJSs的采样控制问题．根据一种连续的MJSs模型和Lyapunov-Krasovskii稳定性定理,通过引入两个可调参数,首先把整个采样区间分段成了四个部分,基于四个采样区间提出了相应的两个状态空间表达式,利用这两个状态空间表达式,构建了一种能够充分利用四个分段区间状态信息的新颖Lyapunov-Krasovskii泛函,再利用积分不等式方法去估计泛函导数,从而获得采样控制MJSs的全新稳定性判据．最后,给出了一个非线性质量弹簧阻尼器系统例子和一个实际的船舶定位系统例子,经过建立仿真,所得到的采样区间最大值远远大于相似文献的结果,表明了本文方法的优越性． 

Sampled-data control of Markov jump system via a fragmentation functional

Markovian jump systems is a most important mixed stochastic system in practice application,the sampled-data control problem of Markov jump system is studied in this paper.According to a continuous Markov jump system model and Lyapunov-Krasovskii stability theorem,the whole sampling interval is divided into four parts by introducing two adjustable parameters.Based on the four sampling intervals,two corresponding expressions of state space are proposed.Novel Lyapunov-Krasovskii functional which can fally use the status information of four frogmentation interual is built.then,using the integral inequality methods to estimate functional derivative,a new sampled-data control Markov jump system stability criterion is obtained.Finally,an example of a nonlinear mass spring damper system and an actual ship positioning system are given.After the establishment of simulation,the maximum sampling interval obtained is much larger than the results of similar literatures,indicating the superiority of the method.