Stability analysis and synthesis of discrete-time semi-Markov jump singular systems

This paper investigates the sigma-error pth $ (p > 0) $ (p > 0)-moment stability and synthesis problems for a class of discrete-time semi-Markov jump singular systems (DTSMJSSs). In view of the Lyapunov functions approach, we first derive the sigma-error pth $ (p > 0) $ (p > 0)-moment stable behaviour of interested systems. Based on semi-Markov kernel approach and the techniques of eliminating power of matrices (EPMs), we then obtain several LMI conditions for sigma-error mean square stability. Subsequently, due to the time-varying singular E-matrix in DTSMJSSs, two different forms of controller gain are exploited in order to design stabilising state-feedback strategies. In particular, computational analysis and comparison of the proposed control schemes are provided, which shows the numerical complexity of the proposed control schemes is vastly lower than that of the existing literature. Finally, an example has been performed to verify the obtained analytical results.