Quantized feedback stabilization of continuous‐time Markov jump systems under asynchronous control

Abstract

AbstractThis paper addresses a new asynchronous control scheme for continuous‐time Markov jump linear systems (MJLSs). Both controlled system and quantizer are asynchronous with the controller due to the process by which the controller can accurately observe and emit the switching signal being stochastic. The random variable satisfying Bernoulli distribution is introduced to describe this observation. On this basis, two methods are proposed to obtain sufficient conditions for exponential almost sure stability and almost surely asymptotically stability, respectively from the perspective of the linear matrix inequality (LMI). The results are independent of the asynchronous time interval. Finally, a numerical example demonstrates the validity and feasibility of developed theoretical results.