This paper is devoted to the time-varying gain controller synthesis problem for a class of discrete-time piecewise homogeneous semi-Markov jump linear systems (SMJLSs). Both sojourn-time probability mass functions and embedded Markov chain transition probability are simultaneously regulated by high-level Markov chain, which leads to a more general piecewise homogeneous semi-Markov kernel. A novel class of multivariate-dependent Lyapunov function is constructed, which is mode-dependent, elapsed-time-dependent, and variation-dependent. The objective of this paper is to design two classes of time-varying gain controllers, i.e., elapsed-time-dependent controller and finite memory controller under bound sojourn time. Numerically testable stabilization criteria are established for discrete-time piecewise homogeneous SMJLSs via the proposed novel Lyapunov function and two classes of controllers. Furthermore, two desired stabilizing controllers are designed such that the closed-loop system is mean-square stable. Finally, the proposed control strategies are applied to a numerical example and a practical example of solar thermal receiver to show the effectiveness and applicability of the theoretical results.

本文致力于研究一类离散时间分段齐次半马尔可夫跳跃线性系统（SMJLSs）的时变增益控制器综合问题。逗留时间概率质量函数和嵌入马尔可夫链转移概率同时由高级马尔可夫链调节，这导致更一般的分段齐次半马尔可夫核。构造了一类新的多元相关Lyapunov函数，它是模式相关的、经过时间相关的和变化相关的。本文的目的是设计两类时变增益控制器，即消逝时间相关控制器和有限记忆控制器。在限定的逗留时间下。通过提出的新型 Lyapunov 函数和两类控制器，为离散时间分段齐次 SMJLS 建立了数值可测试的稳定标准。此外，设计了两个所需的稳定控制器，使得闭环系统是均方稳定的。最后，将所提出的控制策略应用于太阳能热接收器的数值例子和实际例子中，证明了理论结果的有效性和适用性。