Stabilization of Continuous-Time Probabilistic Logical Networks Under Sampling Dwell Time Constraints

Abstract

This paper investigates the sampled-data stabilization of continuous-time probabilistic logical control networks (CT-PLCNs). CT-PLCNs can provide quantitative and accurate descriptions for the transient kinetics in comparing discrete-time probabilistic logical control networks (DT-PLCNs). First, CT-PLCNs are transformed into switched continuous-time probabilistic logical networks by regarding the control input as a switching signal. In this setup, CT-PLCNs can be classified into two types: one with stable modes and the other with only unstable modes. Then the concept of average l-sample dwell time is proposed to describe the scenario, where the dwell time of each mode is an integral multiple of the sampling period l. Based on this, the stabilization conditions for CT-PLCNs are established by restricting the sampling dwell time of controller modes. Furthermore, a copositive Lyapunov function is constructed for the case with stable modes and is discretized for the case without stable modes, providing a new framework for studying the stabilization of CT-PLCNs. Finally, a chemical model generated by GINsim is provided to demonstrate the feasibility of the obtained theoretical results. Overall, this paper provides new insights into the stabilization of CT-PLCNs and presents practical applications for chemical models.