Stabilization for a class of continuous‐time nonlinear Markov jump systems via the approximate discrete‐time model

Abstract

AbstractIn this paper, a stabilization scheme for a class of continuous‐time nonlinear Markov jump systems is investigated by sampled‐data control mechanism. This stabilization scheme is given in the form of a discrete‐time state feedback controller which is designed based on the approximate discrete‐time model (ADTM) of the original continuous‐time system via the discrete‐time design method. During the process of controller design, an appropriate iteration step size is selected for the ADTM to restore the missing intersampling data due to the sampling characteristics, and this provides the iteration solutions of ADTM to the controller. The introduction of the iteration step size achieves a perfect tradeoff between calculation precision and control cost which not only guarantees the calculation precision of the ADTM, but also reduces sampling frequency effectively. Subsequently, we analyze the consistency condition between the continuous‐time nonlinear Markov jump systems and its ADTM, and give the criterion of the mean‐square exponential stability of the system. Based on this criterion, we prove the mean‐square exponential stability of the closed‐loop sampled‐data system with the designed discrete‐time state feedback controller. Finally, the feasibility and effectiveness of this scheme are clearly verified by a numerical example.