Mean-square stabilisation of discrete-time semi-Markov jump singular systems with mode-dependent singular matrices

This paper investigates the mean-square stabilisation problem for discrete-time semi-Markov jump singular systems with mode-dependent singular matrices. In contrast to the Dynamic Decomposition (DD) method, which introduces high-order dynamics and increases the system dimension, this work adopts the Weierstrass Decomposition to preserve the natural first-order structure. To overcome the complex coupling between mode transitions in Weierstrass Decomposition, a scalar-bounded decoupling technique is introduced. Based on this, a reduced-dimension matrix restoration approach is developed to map the stability conditions back to the original parameter space. Consequently, this framework establishes strict linear matrix inequality criteria for mode-dependent state-feedback controllers. It significantly reduces the number of auxiliary matrix variables from O(N2) in DD-based approaches to O(N). Finally, the proposed method is applied to a practical DC motor system. The results verify that the designed controller can effectively manage the sudden degeneration of dynamic states into purely algebraic constraints during topological variations, demonstrating both physical applicability and significant computational advantages.