考虑了相位型半马尔可夫跳变系统的滑模观测器设计问题. 利用补充变量法及模型转化, 将有限相位型半马尔可夫过程转换为其伴随马尔可夫链. 因此, 相位型半马尔可夫跳变系统可等价地转换为其伴随马尔可夫跳变系统. 针对这类系统设计了滑模观测器并给出了观测器可解的充分条件. 最后, 通过数值算例表明了文章给出方法的有效性.

This paper is concerned with the observer-based sliding mode control problem for phase-type semi-Markovian jump systems. Using a supplementary vari- able technique and a plant transformation, a finite phase-type semi-Markov process has been transformed into a finite Markov chain, which is called its associated Markov chain. Consequently, a phase-type semi-Markovian jump system can be equivalently expressed as its associated Markovian system. Then, an observer-based sliding mode control problem is investigated. Sufficient conditions are established for the existence and the solvability of the desired observer. Finally, a numerical example is presented to show effectiveness of the proposed design technique.