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

Abstract

In 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.

An improved approach to synthesis of Markov jump nonlinear systems with generally uncertain transition rates

“…Although the paper considers sector nonlinearity, it only performs a local synchronization analysis of the system without controller synthesis. In the past 3 years, the results on nonlinear MJSs have been gradually enriched; see, for example, [28][29][30][31][32][33][34]. However, these papers consider Lipschitz nonlinearity and the proposed results cannot extend to the more general sector nonlinearity.…”