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

Abstract

This paper investigates the σ-error pth$(p>0)$-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 σ-error pth$(p>0)$-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 σ-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.

Keywords:

• Singular systems
• semi-Markov jump process
• stochastic stability
• control design

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Fundamental Research Funds for the Central Universities [2022FRFK060018] National Natural Science Foundation of China [62173111] Natural Science Foundation of Heilongjiang [YQ2020F006].