Asynchronous control for semi-Markov switching systems with singular perturbation and an improved protocol

This study addresses the asynchronous control problem for a semi-Markov switching system in the presence of singular perturbation and an improved triggering protocol. To decrease the occupation of network resources, an improved protocol is skillfully established by adopting two auxiliary offset variables. Unlike the existing protocols, the established improved protocol is capable of arranging information transmission with more degrees of freedom, thereby reducing the communication frequency and maintaining control performance. Apart from the reported hidden Markov model, a nonhomogeneous hidden semi-Markov model is used to handle the mode mismatch between the systems and controllers. Benefiting from Lyapunov techniques, parameter-dependent sufficient conditions are devised to ensure a stochastically stable subject to a predetermined performance. Finally, the validity and practicability of the theoretical results are verified via a numerical example and a tunnel diode circuit model.