An Improved Jump Model for Two-Dimensional Markov Jump Roesser Systems and Its H ∞ Control
提出了一种改进的二维马尔可夫跳跃系统模型，用两个独立马尔可夫链分别描述水平和垂直方向的动态切换，避免了模式模糊，并设计了状态反馈控制器实现稳定性和H∞性能。
In this study, an improved jump model is proposed for the Roesser-type 2-D Markov jump systems (MJSs). We use two independent Markov chains that propagate along the horizontal and vertical directions, respectively, to characterize the switching of system dynamics in those two directions. Compared with the conventional jump model, which uses only one Markov chain to characterize the switching of system dynamics in both directions, the newly proposed 2-D jump model shows better modeling capabilities for real-world applications with abrupt changes while inherently avoiding the mode ambiguity phenomenon. Based on the proposed jump model, we then propose a dual-mode-dependent state feedback control law to stabilize the concerned 2-D MJS. A sufficient criterion, whose feasibility is enhanced via a dual-mode-dependent Lyapunov functional technique, is obtained to ensure the asymptotic mean square stability and $H_{\infty }$ disturbance attenuation level of the resulting closed-loop system. Subsequently, resorting to a novel nonconservative separation principle, two equivalent conditions with one of them in the form of linear matrix inequalities (LMIs) are developed. Finally, a convex optimization algorithm which is formulated by the obtained LMIs is proposed to design the control law. An example of the Darboux equation with Markov switching parameters is presented to validate the effectiveness of the obtained results.