This paper is concerned with the issue of smooth control for semi-Markov jump linear systems. The performance metric on the control smoothness for general non-deterministic switched systems is renewed for the studied stochastic switched system by exploiting the statistical information including transition probabilities and sojourn-time probability mass functions. The practical asynchronous switching phenomenon in the system is considered. A piecewise control law with flexible duration for control smoothness is proposed as a first attempt, which outperforms the traditional duration that is either less- or over-designed in terms of smoothness. A receding algorithm is developed to eliminate the nonlinearity curse caused by the terms of power of matrices in the derived existence criterion of controller. Illustrative examples including a class of are presented to demonstrate the validity and applicability of the theoretical findings

中文翻译：

---

半马尔可夫跳跃线性系统的灵活持续时间的平滑控制

本文研究的是半马尔可夫跳跃线性系统的平滑控制问题。通过利用包括转移概率和停留时间概率质量函数在内的统计信息，针对所研究的随机切换系统更新了一般非确定性切换系统控制平滑度的性能度量。考虑了系统中实际的异步切换现象。作为首次尝试，提出了一种具有灵活持续时间的分段控制律来实现控制平滑性，该控制律在平滑性方面优于传统持续时间设计过少或过多的控制律。提出了一种后退算法来消除导出的控制器存在准则中由矩阵幂项引起的非线性诅咒。提供了包括一类在内的说明性示例来证明理论研究结果的有效性和适用性